Avalon sometimes waives the single supplement. If you look at the dates and prices of specific cruises, it'll say something like "single supplement waived". It's not hidden, but it is limited.
Gate 1 is also an option. At least one of their ships has single cabins. They're tiny, and in the aquarium, but reasonably affordable. They also have the occasional "no s/s" promotion, but you have to be on their email list. They often have promos offering a couple hundred dollars off, but once in a while I hit the jackpot where the entire single supplement is waived. I don't know if those promos are valid in the UK.