If I were you I would do exactly that - and if you have a bio passport or whatever they're called you can use the machines to go through even quicker.

When you exit the baggage hall you enter the arrival hall, scuzzy as it is, over on the far right is a corridor into departures proper, so it's through there and over to VS UC check-in and up the lift to the private security channel.

As a tip, when the cabin crew come around with immigration fast track vouchers, take one in case the queues for UK / EU passport holders are longer!

You'll get more time in the Clubhouse to relax and clean up, or just grog!