I'm guessing wildly that you'll also need to add new RAM. It's very likely your old RAM is DDR3 and new motherboards and processors generally use DDR4. RAM is unfortunately not cheap now, so, I don't know what to suggest on such a tight budget. You can always go for an older generation motherboard/processor. Though, that would probably limit you to something AMD AM2+ related, which is a 3+ year old design. From the days when AMD were really struggling to keep up with Intel.
(edit)
Slightly elaborated: You can get an AMD Ryzen 3 plus a budget micro ATX motherboard for less than £150. The problem is, the only RAM you'd be able to get for that, and stay below 220 quid is a 4GB stick. You can obviously gamble a bit and hope that the next 4GB stick you buy when you can afford it is hardware layer compatible with your first one, keeping performance optimal. That is a gamble, though. Worst case scenario is that you'd have to buy two new replacement memory sticks (again), once you'd want to upgrade beyond 4GB.