yes, u can buy a 3-day travelpass as the first answer said. but it only include zone 1&2, if u want to go/from heathrow airport or other airport, u have to buy a ticket from zone 6..... or u can buy one day LT card which allow u to take bus, subway, light railway within zone 1-6... 8.20pound (price may be not updated)
for both destination and travel, u can buy a londonpass, detail see the web
https://www.londonpass.com/index_attractions.asp
it is quite expensive but u can enter most of the london destination for free and also transportation in zone1-6. u can choose 1, 2, 3,6days....
give u a tip, u dont need to buy londonpass for 3 days, u can buy for 2 days and the third day buy a one-day travelpass to somewhere u dont need to pay.
for the b&b of rome, here is the web
http://www.babredrose.com/home.html
the location is quite good because it is just 3-5mins walk to the subway and very close the Colosseum(鬥瘦場). u can take subway to other major tourist destinations easily.
hope it can help. wish u have a nice trip
參考: experience: studied in switzerland for 5 yrs. have been 30 countries in europe.