It’s not a simple as simply turning it back on , on what basis did you initially ‘leave’ ?, were you simply ceasing your service at your old address and using some other company at the new address or were you using the home mover service and taking a BT service at your new address ?
If simply ceasing then obviously turning it back on after it was switched off on the date you gave ( even if that date through no fault if your own has changed ) re establishing service would be a new contract and possibly require the usual lead times etc ..if you used the BT home mover , then obviously your new service at the new address will presumably also be affected by the change of date
