Hotpoint spin cycle no longer working.

I have a Hotpoint washing machine. The drum spins perfectly during the wash, but when it comes to the spin cycle it doesn't work. It drains perfectly well, too.

I usually have the spin set to the max 1600rpm, but any speed setting I've tried isn't working, it just slowly spins in alternating directions at the normal wash rate.

Edit: I failed to mention that the water wasn't draining properly a few days ago so I opened it up and removed a lot of debris from the filter.

Maybe I've unintentionally done something to make the washing machine think there's always water in the drum or something like that, so it refuses to start the spin cycle, even when it's empty and dry.

I've checked the pipes and the wiring round the back, everything seems to be as it was before I touched it.