Actually, the Joie Versatrax or the Joie Finiti were the first that came to mind when you needed a pushchair with a reversible seat configuration right from birth. A Versatrax pushchair can be, however, bought from £295 which is slightly over your budget - but I would still think about it as, at this price point, it is one of the better choices out there. You CAN use it from birth even with the seat, even though I strongly recommend a very good footmuff or a cocoon kind of soft-carrycot to put in.
Next in line, for such a low budget, I would actually think about a 2in1 solution where the carrycot converts to a seat unit, which will work for you at least the first 1.5 to 2 years of age. These usually have shorter seat lengths and are not the best with large, tall toddlers, but for the price are very good starting prams + pushchairs and can be sold afterward, making place and budget for the next, lighter and more compact forward-facing only buggy. My suggestions here would be something in the likes of Kinderkraft Juli or a Maxi-Cosi Zelia. You won't have to store the carrycot while still having a sort of lie-flat bassinet at hand in the first months.
My last idea here would be very very nice to push Quinny Zapp Flex Plus reversible pushchair combined with the Quinny cocoon making the bucket-seat surface flat and cozy for a newborn. The buggy + cocoon together would be about £288 and it's a quality, reasonably compact, and a super-spacious pushchair that will last you at least 3 to 4 years.