It seems I was wrong to think the worst of BT. Download speeds are back to normal for the last couple of days...

It's never wrong to think the worst of BT. They were probably fiddling with something and didn't want to tell anyone.

Do BT still have that stupid billing policy of charging you the correct amount every quarter or making you pay a fixed amount every month which is never quite correct?

no
i have a pay monthly DD set up for BT which takes the amount owed each month
so there is complete settlement each month for the whole bill
which includes phone/broadband, line rental i pay annually in one lump sum ...

Actually yes they do, just like the majority of utility providers. And if I'm not mistaken you actually get charged more for paying quarterly anyway (or rather you get charged less for paying monthly).
Generally speaking I quite like a fixed monthly DD as it makes it easy to budget but it does mean you have to be aware of how the DD amount is working out in practice against your actual usage. Most utility companies will only review things once a year unless you poke them with a stick and unless you've stayed on top of things the adjustment can be a nasty surprise although they normally try to arrange it so you overpay and build up a credit which you have to fight to get back (rather than them offsetting it against future spending).

In BT's case I became very frustrated by their deliberate refusal to adjust DD's when they varied their prices unless challenged.
For example, and this is what made me switch from BT:
I was paying £xx a month for line rental and calling plan which exactly covered all of my phone usage. That was fine.
However, BT then increased their line rental charge but told me that I didn't need to adjust my DD. Well, that was clearly wrong. I also generally object to companies tying you into a contract that lets them vary their prices but doesn't let you leave if they do so.

That should be enough for every customer to change providers. No matter what the service, or how recently you took the contract out.

I do believe that either Ofcom or the OFT are looking into the self same practice (mid-contract price rises) by the mobile companies. Their contracts allow them to raise prices due to inflation once a year regardless of the length of the contract which is incidently why I'm planning to switch to a monthly rolling mobile contract having been stung twice with my current provider on a 24 month contract.

I think that they should be held to the contract for the duration. My current contract is no longer available from Three. It is actually more expensive, but then when I budgeted I treated most of the cost as an interest free loan on the handset. Then compared the call time on the balance. Once the contract is over then they can push prices up but then I might move to another provider. To change the rules when people are still trapped on a contract is simply wrong.

I did. I moved to Plusnet and have never looked back.

Over here, it works the same as a mobile contract, they debit the complete amount each month - line rental, plus all calls that month.

I was with Vermin and their fair usage policies drove me to sky. I only have the broadband but it suits me well.