London for 8 nights

so looking for lots of freebies

National museums are free, though they have heavies who try to twist your arm into making a large donation at the entrance. There are lists available with lots of free things to do, here's a reputable one, but no surprise all those free museums are up at the top of the list. http://www.timeout.com/london/things-to-do/101-things-to-do-in-london-free-things-to-do

Rental-Biking around the city?

You can do that. If you choose the route carefully, it can be fun. For long trajectories you need to go to a bike hire place to hire by the day, that google will find for you. Cycling the Thames Cycleway is good E or W. If you go a long way along it, you can always get a train back, and it would be wise to have a map as you can lose the route, all too easily. For short A to B journeys of up to 30 mins look at Boris Bikes, as Santander Cycles are known by the locals: https://tfl.gov.uk/modes/cycling/santander-cycles If you sign up and pay the basic charge, you can do the 30-min hops for free; if you don't sign up you can pay £2 per 30min hire.

Cheap awesome pubs?

Not available. Of course some London pubs are less expensive than others and some are less unawesome than others, but on the whole awesome pubs are in country villages and cheap ones (for Britain) are in The North, and London has nothing to compare with either. Though if you travel as little as about 40 mins on a train to get to a country area and walk attractive footpaths to country villages you can find awesome pubs, eg in the Chilterns (suggest stations such as Great Missenden and Wendover and Princes Risborough, accessible from London Marylebone Station - or even outer stations on the Metropolitan Line such as Chesham, Chalfont & Latimer, and Chorleywood, to start your country walk - even at the nearest of these you can walk/cycle to pubs like The Cock near Sarratt or The Bedford Arms at Chenies which give you a feeling of being a world away from London) but being up-market commuter areas they won't be cheap there either. Walking/cycling in the Chilterns, of course, is a cheap thing to do once you have got there, a map at 1:25 000 scale is advisable.

Well luckily most of the big (and not so big) museums and galleries are free. The Santander bikes are quite cheap, but be careful because central London isn't exactly bike friendly, especially if you're not used to driving on the left. If the weather is fine then just walking is great free entertainment, there are endless interesting neighborhoods to see. You could hit up some markets (Borough, Camden, Broadway, Spitalfields etc.) for free entertainment and cheapish food.
Weatherspoons are the cheapest pubs, but for me aren't exactly awesome. Sam Smiths pubs used to be cheap and have a better atmosphere but they seem to have raised their prices in the past few years. I wrote a long post about London pubs if you're interested (under my old handle Eurotrash).
Other cheap food can be found in Chinatown, takeaway kebabs or fish & chips (but avoid the famous Rock Sole Plaice in Covent Garden whose prices are extortionate), Brick Lane Beigel Bake does a great salt beef sandwich for under £4 that should fill you up for a while.
You might want to have a look at Time Out for listings of free/cheap events.
Good luck.

they have heavies who try to twist your arm into making a large donation at the entrance

I think Iviehoff is being facetious. I've never made a donation and never felt any pressure to.

I think I'm remembering an earlier time when you were rather more pressurised into donations.

FWIW here are some more interesting London pubs, though none of them is cheap, I sure other people have other favourites:

The Seven Stars, Carey Street, eccentric place, haunt of eccentric lawyers
The Nell Gwyn, tiny pub hidden up a narrow passage between Strand and Maiden Lane
The Ship and Shovell, in a passage under Charing Cross Station, has a footpath through it
The Old Bank of England, Fleet Street, it really is just what it is called, very different
Ye Olde Cheshire Cheese, up a passage just off Fleet Street, cellar-like ambience

There are some lists available to tempt your fancy.
http://londonist.com/2013/12/londons-most-unusual-pubs

there are usually 'London for free' publications and websites kicking around. Don't miss the free museums, nothing like them anywhere else.

and a lot can be done by walking and LOOKING (phone AWAY!).

Here's my personal cheap recommendations:

• Warung East/West - top floor, 57 Charing Cross Road (Chinatown Market) - When you go up the escalators it's not the Indonesian place you see immediately to your left - keep walking a little further. Definitely not glamorous (it's in a shopping mall) but delicious and authentic Indonesian food for £5 a main course. Open from noon to 9pm daily.

• Try one of the street food markets for lunch. Usually stuffed full of office workers, you can usually get something nice for a fiver. Exmouth Market (near Farringdon / Angel) or Whitecross Street Market (near Barbican / Old Street) have always been good to me. For Whitecross Street Market, you can do what a lot of nearby workers do -- take your lunch into the actual Barbican to eat and enjoy some Brutalist architecture at the same time.

• The cheapest pub I know in London is the King William IV in Leyton, which is a Brodie's brewpub. Their own beers are £2.60 a pint (!!). Not bad beer either, and it's a traditional local pub not a slick-looking craft beer bar, albeit not in an especially lovely part of the world.

Their own beers are £2.60 a pint (!!).

Yes that is very cheap for London - my mention of The North was also a bit facetious, in general lower prices are available anywhere really grim that you probably don't want to go to, and grim is available even in London. In central London pubs, beer generally starts around £4 pint. That, and the mention of £5 for filling street food, perhaps scopes for you what counts as cheap in London. You can of course eat much more cheaply if you go to a supermarket and buy basic things.

I made a trek out to the King William IV because Brodie's beer is really good (their black IPA especially). The pub's clientele on the day we went was shall we say... interesting. Leyton gives off the vibe of a pre-gentrification Dalston. No doubt artisan espresso cafes will be opening on the high street and rents will skyrocket before too long.

around 4.50 a pint last month in London and cheapest place found to eat was McD...

Sixteen pounds for sausage and mash in one pub, 4.50 for a sausage roll and fiver for a Scotch Egg.

Cheaper to go to Waitrose, Sainsburys or Tescos for take out meal deals - usually sandwich and a soft drink.