Look Spade you haven't said how much time you plan to spend on this trip. You could run around 8 cities in a couple of days for £800 but what would be the point of that? You need at least £50 a day not including transportation to be able to enjoy your time anywhere. So what does that tell you? That you can spend 8 days on your trip. Given that any time you move from one place to another, you basically use up a day, that means you won't even be spending a day in each place, just travelling between places.
So no it isn't a decent budget for 8 cities. To visit 8 cities you need at least 3 days/4 nights per city plus a travel day between each. That's a total of 31 days. At £50 per day that £1550 plus transportation costs.
With £800 your best bet is go to one place and sit for a week. That you could manage on your budget.