I would avoid any airport in the UK, period, due to the fact that they doubled the departure tax on February 1st. And, LHR is a major hassle, anyway.

I go to Europe every 5 or 6 weeks and use the Star Alliance Airpass, which can only be purchased in the US, BEFORE you leave. It can be on the same day as departure, but it must be prior to departure from the US.

Here's how it works:

It's for as few as 3 and as many as 10 segments within Europe and the Balkans. (I'm sure you can find another city to visit to fill in the extra segments to get back to your starting point, in this case, unfortunately, LHR).

You MUST take the first segment at the time and date you scheduled it for. The first segment kicks off the pass.

Any other segment's time and date can be changed without penalty.

The cost depends on miles flown. 0-249 miles = $65, 250 - 499 miles = $100, 500+ miles = $135. This is NOT including taxes.

If you have not completed all your segments, you can buy additional segments, while in Europe.

If you don't use a segment, tough luck, no refunds.

I have found the Star Alliance to be a good deal, because they have hubs in Munich, Frankfurt, Brussels, Amsterdam and Vienna.

Avoid SAS, they charge you for even water and big $ for food.

Austrian and Lufthansa are pretty good operations and they have food gratis. LOT is pretty good, too.

Vienna is a great hub, because Austrian's lounges have really good free food and free wireless. I go out of my way to fly Austrian and route through Vienna.

AVOID, AVOID, AVOID LHR, if you can. See if you can change your United flight destination to one of the other hubs.

Good luck.