Jae,
First and most important .. its a football match ... especially near Man U fans ... soccer is a game the Americans invented for their girls!! I think the chances of you getting a ticket for Man Utd for a home match are very remote as most of the games are sold out, a better chance would be to see an away match unfortunately they are not playing any of the London teams during October. If you have more exact dates I'll see who they are playing during that period any if there is any chance of tickets but I expect that you will have to travel out of London to see them. As regards sights in London there are a myriad of companies that will do tours etc however if you have an idea of what you want to see and it is primarily in Greater London then the best bet is to do it yourself on public transport. London Underground is the fastest way to get around London as traffic can be horrendous at times and most tours use coaches and the roads. You can get an all day rover ticket valid on all London public transport for about USD 10. If the sights are outside of London then a tour may be the best option however the rail companies also offer 'Days out from London' packages to certain locations. I'm not too informed on castles and gardens however I know that within Greater London Hampton Court Palace is famous for its buildings and gardens and also there are the famous Kew Gardens. There is more information on the Royal palaces at <a href="http://www.hrp.org.uk/webcode/home.asp" target="_blank">http://www.hrp.org.uk/webcode/home.asp</A> which has details of multi-site ticket deals or for garden info try the Royal Horticultural site at <a href="http://www.rhs.org.uk/" target="_blank">http://www.rhs.org.uk/</A>.
Just outside of London in Maidstone you also have Leeds Castle ( which is in Kent and not Yorkshire as might be thought from its name ).
If you have an specific sites you are thinking of then let me know and I'll see what I can find out in respect of them.
For general info about trips to London you might also want to check out the posts of my predecessor in the forum by searching for 'Former Nonrev Correspondent - London'.