Lovely room in lovely area no holding deposit

Looking for someone or a couple would be (£1300 pcm)to take over my lovely double bedroom in a shared Fulham flat. Great location, close to shops, parks, and transport links. Friendly housemate, spacious living area, and a great vibe. I am sharing with my friend she is 26 and she is never really at home, there is big kitchen and separate living room all the bills will be shared half and half

Bills usually are £138 council pcm
Gas& electric round £80 pcm ( winter the most we paid £ 130)
Water £40

Move in would be straight forward
1) 3 month bank statements
2) pay two month up front - if is single person £2400 let’s say if you move in the first of may then next payment will be July the 1 st there is no holding deposit
3) reference from previous landlord