You are technically 'allowed' to do anything and they have to support you. I think the concern with twins is the average NHS midwife team probably doesn't have anyone who has supported a twin home birth before, though independent midwives will have more experience. It's more just that it isn't common, so they might feel hesitant and you might also feel hesitant with someone who isn't confident in their skills. You are more likely to find an independent midwife who has done one or several twin home births, and if you can afford it, I would take that route personally if it turns out you're having twins and you want to have a home birth with twins. But if it comes to that, you can also just raise it with your local home birth team and get a sense of whether they have done one before and how comfortable they would feel supporting you at home. In theory, they have to support you if it's your choice, but if you talk about it with them, they may be able to find you someone who does have experience and steer you into their care. You might also consider using NHS midwives for your antenatal care and then just use an IM for the birth, some will arrange something like that if cost is an issue. I'd recommend finding the Facebook group Home Birth Chat UK. There are plenty of ladies on there who have had twin home births, and I'm sure some have done it on the NHS, so might be able to offer you some advice if it does turn out you're having twins. It's also just helpful in general for planning a home birth.
That said, at 8 weeks with my first, I was huge, probably almost as big as I was when I was in 3rd tri and it was all bloat. Everyone who knew at that point was sure I was having twins (twins run in my family), but it was just because I was bloated. It went away by about 14 weeks and my daughter (just one) was a tiny 6lbs 9 oz at birth so not even a big baby.