Hi breaky9765 -
The Thames Path is a national trail so thus has a website under nationaltrails.com and there is a small section on baggage transfer which includes the aforementioned ridgeway and one other company ‘Move My Bags’ - both can be e-mailed direct from the site.
There’s also been a similar enquiry on this forum before and one other piece of advice was to move the bags each day by taxi. This might not be a bad idea as I have recently explored using baggage transfer on another national trail (The Pennine Way). While there was no shortage of companies I found the likely costs prohibitive. That said the PW is a three week walk for me and visits remote areas - the locations also have a direct bearing on cost. After due consideration we abandoned the idea of transfers and decided to carry our own gear, with a ‘restock’ at halfway courtesy of a ‘conscripted’ friend!
You obviously are unlikely to have the option of carrying your own gear but you won’t be too far off the beaten track on this walk, so hopefully one or all the companies will be able to quote you more reasonable costs.
Good Luck with the walk, hope you have a great time. Do let us know how you got on with a Trip Report!