Traditional wedding cake is a heavy fruitcake with that hard white icing stuff on it.
I think the point was to have a cake that kept a long time, whereby you would post off a piece (in little boxes) to people who couldn't make it to the wedding.
I got married over here, and like your situation - my English husband had no clue about UK weddings, so he just left it all up to me. I didn't think to ask anyone & just went about things in the way I knew.
People were a bit surprised (in a good way!) about our wedding cake which was chocolate sponge with vanilla buttercream icing, and rather than a cake topper, it just had (edible) summer fruits decorating it all over...with some flowers around it on the cake table. Everyone (majority was English folks at our wedding) said how much they loved the cake so much more than traditional English wedding cake (i.e., the indestructable fruit cake).
We also did the (very American) thing of stuffing cake in each other's gobs - and people here were surprised about that too, but thought it was funny (and fun) all the same.
Initially, we weren't going to register anywhere (for gifts) because DH didn't want to & I wasn't sure. However, pretty much everyone kept asking where we were registered (especially his mum), so we ended up doing it - bonus!
It seemed to be expected among the guests & nobody thought anything (like oh you're being cheeky/greedy/etc) about it - just liked that buying us a gift was easy.
We had a small do (only 20 people in all, including us), and I don't think anyone wore a hat! Lol!
If you're short on funds, it's not uncommon here to have a reception after the ceremony at a pub! I've known several folks who have done this. The Leeds register office is in our lovely Victorian-era architecture Town Hall, and one of my favourite pubs (also from the Victorian era) is across the street from the back of Town Hall - I often see wedding parties in there!
I'm excited because we're off to a wedding reception/party next Friday (Friday the 13th - on purpose!) for one of my work colleagues. He & his wife-to-be are bit on the alternative/wild side, so they have rented out an empty building shell/hall, which is going to be decorated, and the live entertainment is going to be cabaret and burlesque dancers. It's BYOB with an offie just up the street!