Provide you keep your BT Broadband account active, and access your email on a regular basis, then you should be able to use your mobile to connect.
Not sure about the delay issue, so I will ask advice.
I have asked a moderator to provide assistance, they will post an invite on this thread.
They are the only BT employees on this forum, and are based in the UK.
@Beth49 Welcome to the community and thanks for your question regarding your home move. When you move out will you have a date when you will want your service to be activated in your new home or is that still up in the air?
@Beth49 To place a home move order and transfer your existing services from one property to another we need to know the start date in your new home as that's the only way the system will accept the order.
Alternatively you could request the services be moved to your temporary address but there may be a connection charge depending if there is any engineering work required to connect that property. You could then request a home move again when you know the dates when you will be moving into your new home which may also require a connection charge but this may not be needed if there is already a line in place.
The other option would be to cancel your current services when you move out if your not in contract, the email will work for 60 days before its deleted. If you need to you could take out a premium mail subscription costing £7.50 per month to keep the email active. Once you have your move dates you could request to be reconnected at your new home and transfer the email over to the new broadband connection. This however would mean you wouldn't have a broadband connection in your temporary address.
If you speak to the Home movers team on 0800 800 150 they'll be able to discuss the best option to suit your needs.