I'd be careful about going to banks on your own - I guess going to your own would be OK - but my mum was advised not to get quotes (or whatever they're called) from lots of different banks, else they might look at all the searches on your credit rating and wonder why no-one has given you a mortgage.
I got my mortgage with a 5% deposit. It was a few years ago now (2010) so not Help to Buy. I got shared equity, which I think is basically the same thing but, I think, shared equity is only for first time buyers.
I went to a mortgage broker. She got me a really good deal. She wasn't local - she was recommended to me by the sales executive for the development I was buying my house on. I did everything over the phone and via email, never met her in person, but they were all lovely that I spoke to on the phone or email, and very helpful. And even though I only had a 5% deposit, I got the same rate as someone who had a 25% deposit as the bank only had to loan me 75% of the purchase price. My current interest rate is 3.79% and I pay about £400 per month