Not all corect. It should be like this as follow: 我也喜欢周末去伦敦逛逛。

Yes, It's ok here. Also, you can say ‘我也喜欢周末的时候去伦敦 游览/游玩/逛逛。' more nautual. The word 'sightseeing' here means you will not only go to london but also see some views there, in this situation, ’游览/游玩‘ would be better when you translate it. But, most of time, we use 逛逛 instead 游览/游玩 to express our words. Compare with 游览/游玩, 逛逛 means you are feeling more free about the trip and very happy, not just to do some schedule things.

It's perfect, very native!