You do NOT need to close your Halifax account to move to NatWest. Yes, you need to pay in £1k per month for 3 months to get your miles. But that does not have to come from your salary! You can open the NatWest account and go into a branch once a month and pay in a cheque from a savings account.
A few months later, they will write to you and offer you a further 5,000 bonus miles if you choose to close your other account and transfer all your direct debits etc over to NatWest. You will know by this point whether or not you want to leave Halifax. There are a few threads from people who have done this if you do a search under NatWest.
For what its worth, my parents always believed that you should have a track record with a bank, and opened an Abbey National account for me when I was born so that I would have less hassles getting a mortgage when I grew up. The world has changed. A track record with your bank counts for absolutely nothing, unless you run up unauthorised overdrafts etc when a good record may work in your favour in having the fine reduced. But so far as getting a mortgage, loan, credit card etc goes, you are wasting your time building a track record.
Also note ... Halifax's current account pays 3% interest, NatWest pays 0.1%.