I am a HA tenant.
He will not certainly have been evicted for non-payment of three months' rent. They will have advised in a letter that this is a possible final outcome if he doesn't contact them and work with them to clear the arrears. Usually they can set up a payment arrangement/plan and can advise on any housing benefits he might be able to apply for.
They will evict him for if he is breaking the tenancy agreement, dealing drugs, etc., but there would have to be a lot of arrears before they actually moved to evict on non-payment of rent alone. Someone in our street WAS evicted with the reason given as non-payment of rent (there were other issues as well), but I heard that their arrears racked up to nearly £20,000 before the HA actually went to court. The HA have to explore every possibility to keep tenants (even grim ones) in situ before evicting them.
He (and you) ought to keep in mind that if he is foolish enough to get evicted, that will stay on his record, making it very VERY difficult for him to get another HA property in future. His rent isn't even one third of his income - where the hell is his money going? Pans don't cost that much.
It's a hard thing for a single person to get a HA property these days. I was on the waiting list for more than 8 years. I would strongly urge your boyfriend to contact his HA as soon as possible and resolve this with them.
Don't accept any more gifts until he has started making even token payments to, or spoken with his HA. Look at similar local private rental properties? I doubt there are many he'd like that only cost £500 per month.
And, as others have suggested, really think hard about whether someone this reckless with money and responsibility is someone that you want to share your life with.