Assuming this is an ISP switch then I believe so. I haven't switched for a few years but usually, when you place the order with BT it will default to 14 days time, but you can amend that to a later date. You can go through the order process to check before you commit.
Its important that you do not cancel your Sky contract, jus let BT take over the service, and they inform Sky.
If you cancel Sky, that will cause a cease to be issued which will delay any switching.
How will I switch the TV then?. Just ring up and cancel that?
I would expect that to be totally separate assuming its a satellite connection, so you would have to cancel that yourself.
If you intend to use BT TV, then make sure you have a good FreeView signal from a TV aerial.
I would be inclined to just place the broadband order, let that switch & then cancel the TV. That way there's no room for confusion unless they cancel the TV as well, which is what you want anyway. It means paying for another month of TV services from Sky but that gives you a month to ensure everything is working with BT TV before losing Sky.
Once Sky see the order to switch broadband they may well be in contact to make you an offer you can't refuse to stay. In which case you can just cancel the BT order.
1. Usually you can select a start date for your new broadband.
2. Have you checked if you can get FTTP (Full Fibre/Ultrafast) as well? As in, when you put your postcode into the Broadband Availability checker, does it show FTTP products too?
3. In the case of FTTP, there is (usually) the option to select a start date from about 14 days into the future onward.
4. If it's a switch from FTTC to FTTC broadband, you usually just sign up with the new provider and it automatically ends the broadband contract with the old provider through the switching process. Regarding TV though, I would say like you mentioned, probably best to give notice with the old provider to ensure you know when your bills stop with them etc.