Upvote:1
It's not required to include your proof of accommodation in the UK in your Schengen application, but if you believe that including it makes your application stronger, you should include it.
For example, if your accommodation in the UK is inexpensive or free of charge, including evidence of that will make it more likely that the Schengen visa officer will believe that you are able to afford your trip.
To put it in terms of the Schengen Visa Code, any evidence of your total costs for the trip can fall under Article 14(1)(c),
documents indicating that the applicant possesses sufficient means of subsistence both for the duration of the intended stay and for the return to his country of origin or residence, [...] in accordance with Article 5(1)(c) and (3) of the Schengen Borders Code;