Moscow may be the center of Russia, but there are two other really good options here:

Petersburg - LHR-LED on BA or Rossija (or Lufthansa) then LED-VOG on Rossija. Service runs on Sundays and Fridays. LED-VOG is also possible on something called VolgaAviaEkspress. They run now 5 days a week.

Kaliningrad - LGW-KGD on KD Avia and KGD-VOG on KD Avia. Tickets can be purchased online easily on their site (which is in English and easy to use). They run every day of the week except Wednesdays on new, shiny Boeing 737s. You'll arrive in Volgograd at 3:20am, unfortunately. But the transfer will be easy and the company is pretty respectable. They even offer e-tickets! (A major WOW for Russia). The major downside for you is that they fly from Gatwick.

I suppose one might also look at flying from LHR-KGD on Lot or Lufthansa or something

Also, another option to possibly consider depending on your adventurousness is that crazy VolgaAviaEkspress. I've never heard of them or used them, but I'm intrigued by their flights to Volgograd. Unfortunately, their site seems to be only in Russian, but there is a number to call. Looks like they'd be around $250 one-way from Petersburg to Volgograd or about 3900 rubles ($170) from Domodedovo. They have between 3 and 4 flights a day DMD-VOG at 9:45am, 4:10pm, 9:00pm and 10:20pm.

Those are your options: my conclusions - Aeroflot is probably the first thing I would consider (esp since they are having a sale on Volgograd flight this summer). S7 is probably the second thing I would do (they are cheap and reliable), but there are other routes to consider.