You need to do all the soil preparation first to get a half decent looking lawn (and this is the wrong time of year to be laying turf - regardless of the gardening adverts on TV)

There are several methods of clearing the twitch - search the Internet for 'twitch grass'. Basically you have a 4-6 month job ahead of you to clear the soil of one type of grass and exchange it for another type. But at least you'll be laying the turf at the right time of year.

Clear instructions for twitch can be found at http://www.gardenaction.co.uk/allotment/couch-grass-1.asp but this is based on someone wanting to clear the soil for veg.