I "used" a tutor for my DD. I say "used" because I wanted to know what a tutor would do that I wouldn't have thought of.
The tutor made me book and pay for a minimum of 4 sessions, gave me a list of books to purchase and told me I had to stay during the sessions (which were at her house) because she was not a baby sitter

She did no more than I would have done myself except she gave DD homework - eg. make lists of words she didn't know when reading and look them up in a dictionary (I just explained to DD the meanings when she was reading), read "Cargoes" by John Masefield and write a short essay what it was all about etc.
When I told her we weren't having any more sessions I was told DD "was the weakest link in her cohort, not to expect her to qualify and I was being unjust to my daughter for not giving the education she deserved". We continued to use the books at home and booked one mock test for DD so she could familiarise herself with test conditions. This resulted in DD qualifying for the girls schools.
Talk to your DD and ask yourself/DD some questions...How is your DD performing at Primary School? Is she above average? Why do you think she needs a tutor? Why do you want her to go to a GS? Why is her heart not set on a GS? Does she want to stay local? Have you looked a the 11+ material she has been working on - is she flourishing?
Other things to consider when choosing a school - transport available (inc. time and cost), after school activities, parents attendance at events, impressions when visiting schools, attitude of teachers, content (and honesty) of Head's talk, facilities, subjects offered, pastoral care and support, GCSE/A-level results and everyone's bug-bear - Ofstead reports.
I have no experience of Tewkesbury School, but whichever school she goes to, she will only "get out, what she puts in". I know Comprehensive educated children who have achieved fantastic degrees at Uni, just as I know GS educated children who have dismal GCSE results, no ambition and are drifting from job-to-job.