I think it depends on how long you think you will realistically have to wait.
When you say you'd be happy with a small cheap wedding, do you mean you'd be happy to go down to the registry office and just get hitched in front of your immediate family, or do you mean you'd still want a "proper wedding" but not a very expensive one?
If you still want a "proper wedding" where you'll have a decent number of family and friends for food and drink and dancing then even a budget one is going to put quite a hole in your house deposit. Not to mention the fact that I think venue availability is going to be a potential problem with all the people who have had to postpone their weddings this year rebooking for next year.
I think you need to work out how much money you need for the deposit and how much money you need for the wedding and then calculate how long it will take you to save up that money. Where does that put you in terms of TTC?
If you think you'd be starting in a year or 18 months' time then maying waiting wouldn't be too much of a risk. In any case, you haven't been with your partner all that long and if you've only just started living together then you probably want to be doing that for a while (I'd say a year or thereabouts) before you commit to having a child together. If you've only just moved in together then you still have a lot to learn about each other.
That said, I wouldn't wait too long. If you think you need more than 18 months to get on the property ladder and get married, you might want to think about prioritising TTC over one or the other.
I am 34 and have been TTC for a year. Before that I'd been tracking my ovulation and had been off hormonal contraceptives for three years. I ovulate consistently and although my FSH is a tiny bit higher and my AMH a tiny bit lower than I would like, I have a good antral follicle count and my doctor says my ovarian reserve is good. My husband has excellent quality sperm. I've had four early miscarriages and so far no one has been able to figure out what the problem is. I wish I'd started trying sooner.