If you transfer a property or an interest in that property to another person, there will be no stamp duty land tax to pay so long as there is no exchange of cash involved or no transfer of mortgage responsibility. Take a look here
for some example scenarios.
It would seem to me that if you become 50:50 owners after the remortgage to £620,000, then there will be stamp duty to pay on £310,000 (£620,000 @ 50%) which would equate to £5,500. I used the calculator here
to compute the charge.
As the transfer into joint names will occur whilst the property is not the main residence of either of you, the property will not have been your wife's main home at any point during her ownership of it (unless you move back in) and, therefore, she will not be entitled to any main residence relief or letting relief on her share of any gain should you sell it in the future. Take a look here
for confirmation of that.
I hope this helps but let me know if you have any further questions.