I can confirm AAISP are extremely good. But be aware of what you are signing up to in terms of their unit-based tariff and peak-time usage. Basically, if you use the connection a lot from 9am to 6pm weekdays, don't do it as the charges will be quite beefy. AAISP also offer a Home::1 package that is not based on units but instead X Gb per month. Depending on your monthly usage, you may want to consider that instead. You can move the phone line to them, but be aware that it is a locked down line and you cannot make any chargeable calls on it. You can still dial freephone numbers though and receive incoming calls without issues.
I'm probably going to move to Zen next month (my FTTC contract is up). I have used them before, several years ago. They currently offer unlimited fibre 1 and 2 packages (no metering) for a great deal if you also move the phone line to them (which I will be doing if I migrate to them). In this case, they do allow you to make outbound calls on the phone line but charge accordingly for that (see their website for pricing).
There is also Plusnet, but the current negative reports of customer service on the forums here for them doesn't look appealing. And also the fact they traffic manage and block certain sites. But if you don't mind this, they are a cheaper alternative, also with some attractive phone packages to boot.
There is also IDNet, but they also meter your traffic. Vivaciti and Aquiss are others but you would need to compare if you would be getting a better deal moving the line back to BT with broadband from these or letting these ISPs take on the phone line as well as the broadband (assuming they can do that) and paying your pennies to just a single entity.