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I'm gonna guess that someone on here might lend you some of the bits that you after*, I think you might be lucky for someone to lend a sleeping bag.
If you're still struggling and like amey you live in South East London might I suggest that you visit Decathlon as their own brand kit is pretty good and won't break the bank.
Also a 2-3 season sleeping bag will pack considerably smaller than something for zero degrees. If you were still concerned about warmth then get a silk sleeping bag liner, it'll make it much warmer and packs down very small.
@furious_tiles I am a mere disciple of @amey
:D
But I guess better to be on the safe side (and honestly : I am from India and we lot feel cold much more easily than others :D )