Normally you try and do both at the same time. You would need to have your house on the market before the agent for your intended purchase will take you seriously.
Most people then try and close the sale and purchase on the same day - so they have no bridging costs. But this can be risky as there could be a delay and you're left in the removal van with nowhere to go!
Easiest (logistically) is to close purchase and then a few days later close the sale - but it obviously costs more as you have to finance (bridge) the 2 houses for the couple of days.
Or sell first and then close the purchase - if you have somewhere to stay in the meantime. Means you're effectively moving twice!
IMHO if you can afford to bridge you should - it takes all the hassle out of moving.
Normally if you sell your PPR there's no SD clawback - I don't know if there are different rules for Affordable houses. I think there's a clawback of the discount you received on the original purchase though - check with the solicitor who looked after it (or with the relevant council).
Your new purchase will not be eligible for FTB relief as one of you is no longer a FTB (makes no difference whether your fiancee is a FTB)