To not expect neighbour to use washing machine overnight

Sorry, YABU. You can’t tell someone when to do their washing, and it may well be cheaper for them to do it overnight.

If you’re in a terraced house you have to expect some level of neighbour noise, and in the great scheme of things, a washing machine and tumble drier is hardly a big issue.

Good luck if you decide to report it to the HA.
I've been a leaseholder to two HAs and they will do absolutely anything to avoid sorting anything out.
I don't think this is too bad and compared to the frustration of dealing with a HA, I think I'd learn to live with it!

Washing machine in cellar-neighbours never complained.

YABU for feeling it necessary to mention they’re in social housing

YANBU. Earplugs won’t help—it’s about the vibrations not the sound.

YABU. I am struggling to understand how your bedroom is over their kitchen when you are in terraced houses not flats.

And no it is not relevant that you own your house and they are housing association. Are lesser people (in your mind) not supposed to wash clothes? It is perfectly normal to put washing on at 10pm.

My brother sets his machine to go on at 6am I think as he has economy 7 so it costs more to do washing during the day. Would you be more amenable to an early morning wash rather than a late at night one?

My neighbour was 2/3 in the morning

I often wonder how many of the people who say 'use earplugs' have actually had to use them or tried to use them. I tried because I was in a similar situation to the OP and found them really uncomfortable and in the end gave up.

YANBU I have been there with my ex neighbour and it was very annoying. I don’t know how people can say YABU if you haven’t had to deal with this. Remember everything is quieter at night.

I don't think putting a washing machine on at 10pm can be considered antisocial although I get it's causing you sleep deprivation.

Can you move your bed so it's against a different wall? Lay down thicker underlay? Try meditative practices to help you fall into a sleep state or try earbuds?

"but it isn’t unreasonable for them to use their appliances when it suits them."

Maybe it is if it disturbs the neighbours though?

YANBU. Do people really put their washing machines on at night? It sounds very unreasonable.

Just have the groundskeeper shoot them if they come onto your lands, your Ladyship. Bloody peasants.

Most leases have a clause prohibiting noise audible outside the property after a stated time, usually, but not always, 11pm. If next door is a housing association let, they will have this in their tenancy agreement.
However, as another poster said, they might not be aware how loud it sounds in your house. Ask them round to listen to it. They are clearly willing to adjust to some extent, so it may be that once they hear for themselves how bad it is they'll be more likely to stop doing it.
Otherwise, I'd be knocking on their door at midnight asking them to stop. Every time.
Btw, I'm wondering why their washing takes 3 hours? Mine takes 1 hour.

YANBU

When people decide to live in close proximity to others, they accept to be reasonable.

Night noise is not reasonable, and it's not acceptable to put the machines on or hoover at 3am. You can make noise complaints for exactly that reason, but you have better chance of a quicker resolution with social tenants, not much is done with private owners.

You shouldn't have to sleep in the day because of their night noise , especially when their noise then makes it impossible anyway

Yes this would get to me OP its partly the reason that this time we chose an apartment over potentially noisy house..Id spent a year living in what seemed like our ideal house ruined by dog noise intermittently throughout the night..
I used soft earplugs, noise cancelling headphones (and valium when i had to).
Ended up horridly anxious anticipating broken sleep and noise, nearly drove me mad.
Our new apartment complex is fantastic and has strict body corporate rules!. Nothing hanging from balcony, no noise before 7 and after 10pm. No-one in the pool before 7am ..nothing moored to jetty..a few people complain but most move here to enjoy the peace!
In your situation its hard a washing machine is normal family business-and in such close confines as a terrace i imagine the sound does carry. I think pick your battles though-this may not end well for you..

YABU. Living close to other people can be difficult, but it isn’t unreasonable for them to use their appliances when it suits them.

If you can’t reasonably change other people’s behaviour, then you must change yours. Since you own your own home, changing insulation, wearing ear plugs etc.

Needing total silence to sleep or read is a recipe for trouble, you need to work on accepting some background noise. Either that or get RAF Luton on the blower and order an air strike.

It's probably more the vibrations than the actual sound. It might be unbalanced. What is the sound like, OP? It may be fixable.

If it’s relevant we own our house and their house is social housing.

No it's not relevant. But you had to get the dig in.

Of course it's relevant. If they own their house, there's pretty much nothing you can do! If they rent privately, their landlord MIGHT be helpful or might not. It if social housing, the councils tend to be better to deal with neighbours issues. Not enough, but some are.

How is their kitchen below your bedroom when you both live in separate terraced houses? I can’t picture it at all

Very common round here as back to back houses are built on hills. It's called a flying freehold. In our old house we had someone's kitchen under our living room.