JobJar

When you transfer a domain name between registrars all the domain records should stay intact as they are now.
 
So yes, if it's a .uk name then just change the IPStag.

It depends what you want the end result to be.
 
IPS Tag - This is the registrar tag of who manages the domain, who you pay to renew the domain (Currently BT?).
DNS - This is the server which holds all the ip addresses for a records, mx etc.
 
Different hosts have different default settings when you add the domain and then point the dns to them, some keep the mx and a records in tact, some annoyingly default to their own.
 
 
The safest way is to set up all the records on GoDaddy (mx etc) exactly as they are with BT, then do a DNS change to GoDaddy and in theory nothing should happen, everything will work as it is. Then when you want to launch the new site hosted on GoDaddy simply change the ip for the www and default.
 
Edit: Forgot to say make sure you sort out the SPF records etc for the email, 365 setups often lead to honest emails being marked as spam if these aren't correct.