Anya welcome. Do have a browse around the forum, especially perhaps on the section at the end on Mental Health - sadly, you will find that you are not the only one coping with a family member with depression and assorted such afflictions (eg, chronic anxiety, etc).
Do ensure that now you are in the UK you are signed up with a GP, as the GP will be your gateway to the rest of the NHS, and, for your boyfriend, the mental health services that are (sometimes!) availalble. (You may find them not as good as in Germany, as the NHS is under huge financial stress in the UK, and Mental Health is one of the casualties, with long waits and a heavy preference for pharmaceutical approaches - because they are cheaper! - than therapy/psychoanalysis etc etc)
In practical terms, I would say, sign up with a GP for BOTH of you and then maybe YOU go and see them first and tell them your boyfriend has a history of depression, and ask what might be available by way of help for him. From what (not much) I know, I believe that first of all he will be put on a course of anti-depressants, to 'stabilise' his moods, and hopefully 'lift' him a little, and then once he's been on that for say six weeks, he can (I hope) see a therapist to have some 'talking therapy'. I believe the NHS does not do 'talking therapy' until and unless he has taken anti-depressants, as the psychs are so overworked they have to have the meds (medications - ie, pills) give them a 'head start' on treatment.
May I ask if English is your first language (and your boyfriend's) as if it isn't, then 'talking therapy' might be a little trickier for him??? Just a thought!
In terms of you and him, I'm afraid that my own personal opinion is that he MUST agree to see the medics and take the treatment offered, if you are to stay with him.
Depression is an extremely 'self-absorbed' condition, and those with it can find it hard to understand why others find it difficult to cope with them. They are so focussed on their own unhappiness, and cannot see what it is doing to others (or they do, and that simply adds to their bad feeling about themselves.)
So, in a way, it is up to you to set the boundaries and the 'rules', to stop him sinking further and taking you with him, and, as I say, personally I think you need to make it clear he MUST be 'in treatment' (even if it's not that satisfactory) not sinking more and more at home.
What is happening on the money front? Can he still work? I do hope so! In a way, work itself can be very 'therapeutic', in the sense that sitting at home being unhappy is NOT therapeutic, but it may depend on his abilities.
hopefully things will come together for you both, and this will be a happier time coming soon.