As has been pointed out, you don't actually need a physical branch, not even for paying cheques in. In fact, once you make the leap to mobile banking, you don't even need to put them in the post. You just scan them with your mobile.
I appreciate that this all sounds a bit daunting but, trust me, once you get into the swing of things, you'll wonder how you ever managed before!
I'm making the assumption that you are what we used to call a senior citizen. I'm sure there will be adult education classes locally where you can learn IT skills. You'll never regret it.