There doesn't seem to have been a move for a few years...
In the NFL, at least. Since the Houston Oilers moved to Tennessee, we've seen...
NBA
Vancouver Grizzlies move to Memphis in 2001, becoming the Memphis Grizzlies
Charlotte Hornets move to New Orleans in 2005, becoming the New Orleans Pelicans
Seattle SuperSonics move to Atlanta in 2008, becoming the Atlanta Thunder (a move that violated the agreement in the exchange of ownership)
New Jersey Nets move to Brooklyn in 2012, becoming the Brooklyn Nets
NHL
Hartford Whalers moved to Raleigh in 1997, becoming the Carolina Hurricanes
Atlanta Thrashers move to Winnipeg in 2011, becoming the Winnipeg Jets
MLB
Montreal Expos move to Washington DC in 2005, becoming the Washington Nationals
MLS
San Jose Earthquakes move to Houston in 2006, becoming the Houston Dynamo
There's also been moves in the Arena Football League and the WNBA...but nobody cares.
More important than that, though, is the number of expansion teams added to the leagues in that time period...
NFL
Cleveland Browns (1998)
Houston Texans (2002)
NBA
Charlotte Bobcats (2014)
NHL
Nashville Predators (1998)
Atlanta Thrashers (1999)
Columbus Blue Jackets, Minnesota Wild (2000)
MLB
Arizona Diamondbacks, Tampa Bay Devil Rays (1998)
MLS
Chicago Fire, Miami Fusion (1998)
Chivas USA, Real Salt Lake (2005)
Toronto FC (2007)
San Jose Earthquakes (2008)
Seattle Sounders (2009)
Philidelphia Union (2010)
Portland Timbers, Vancouver Whitecaps (2011)
Montreal Impact (2012)
New York FC (2015)
Checking around online, a lot of comments about the London move aren't complaining about the move, more than the NFL is trying to expand again but do so in the least organic way possible - as well as comments about them being desperate for a franchise based in LA.