Ask your existing tenants to allow viewings during their notice period, this means you could start viewings immediately and only have a few days in between tenancies, as long as there is not a lot of maintenance to be done.
Ensure the property is looking at its very best at the viewing stage. Do not perform a viewing where you are saying, oh this will be done, and I am repainting this purple wall magnolia. For some reason many tenants can often not see past what is in front of them and it will put them off. Show your house in its very best light and it will let quicker.
Think about the offers that are made on the property. Even if you have an offer which is a little less than you would hope think about the cost implications of having the property empty, utilities and the new rules on empty property discounts for council tax. See further details below.