MY preference of the two Istanbul airports for London bound flights is Sabiha Gocken, all contained in a nice modern single terminal. If you fly with Pegasus all the way to the UK then if you choose tyhe right flight the changeover time at the airport is less than an hour. Only problem is that Pegasus only fly in the winter months to Stanstead, rather than Heathrow with but the time saved waiting for the second flight can be won back, and generally Pegasus are cheaper than Turkish airlines, and if I had to choose based on price, quality and staff it would be Pegasus all the time.
The other option of going through Sabiha Gocken is that you can always pick up an easyjet flight to Gatwick or Luton, but the connection time with the Pegasus does mean a lengthy wait at Sabiha Gocken. The again it's not so bad there are plenty of nice areas, and prices are considerably lower than Dalaman ... but then again how hard is that!