Do count that with a limited price and a need for a light, urban stroller, there will be compromises with such a stroller. I am just saying that a lightweight - usually meaning a smaller pushchair or buggy - that should comfortably accommodate a large toddler while being decent for regular use and long-distance strolls is, yeah, quite difficult to get by.
I would, in any case, start with the Oyster Zero that is wide/roomy enough, with a super large canopy and a nice push overall so it should suit you just fine. The only thing might be the price - it's usually around 240 - 250 GBP. It should be, however, not that hard to find a sale or a promotional coupon/voucher. With it being pretty much perfect for you, which is quite rare, it's kind of worth checking everything out (or paying a bit extra to be comfortable).
Apart from maybe a Quinny Zapp Xpress that kind of fits your budget, or a cheaper (but lower quality) Kinderkraft Grande, my next suggestion would be looking for a pre-loved pushchair from a better brand. Maybe a Baby Jogger City Mini would suit you...
Think about it, and either compromise on features, on the price tag, or the novelty of the buggy... Good luck!