I bank with Lloyds and they have all the services you've mentioned, though I don't use all of them so I don't know how good they are.
- Lloyds app has touch ID for the phone. I
do use this, and I like it.
- Assuming it's the same thing as "round up", they offer "Save the Change" service, in which Lloyd's will "work out the amount to the next whole pound and transfer it from your current account to your nominated Lloyds savings account." I'm not enrolled, because I already have standing orders to move amounts into my savings accounts each month, and I don't actually make very many purchases so it'd be a really slow way for me to save. But it's a service that is available.
- For budgeting, they offer "Money Manager" for free. According to their website, Money Manager is a free budgeting tool that lets you "view how you spend your money with easy-to-understand graphs, see most of your spending automatically categorised, and get a better picture of your spending and saving." I don't use it, either, because I keep a spreadsheet for my budgeting. Plus, it seems mostly geared toward tracking and categorizing spending, and I primarily spend money on food (and booze, but that's part of my grocery spending)... categorizing is complete!