Since your phone is unlocked, you have a number of options. EE is the carrier I usually use in the UK, they have the largest network and coverage 4G LTE. Here is a link to their pay as you go SIMs
Their largest data plan is 20 GB for £30 Comes with unlimited texts and lots of phone minutes, but I understand data is really what you’re needing. Vodafone has the exact same offer. The Lyca data only SIMs on their website seemed to be more expensive, but perhaps having experience with them last time outweighs price.
Just curious...Do you need the high daily data because you are using your phone as a hotspot for your other family members? Will their data needs be as high in London when you will all be out seeing the sights? How many days will you be in the UK?
EE has boutiques around London. Both EE and Vodafone SIMs are available at Carphone Warehouse, many locations around London. Hope this helps!