See if you can borrow a box from a retailer
Alternatively, buy one from Argos or Amazon, open very carefully, preserving all packaging so that it can be packed and returned as not suitable/will not work properly. Both are usually very understandable provided care is taken to preserve the as new quality of the item
If you can receive SD Freeview OK with the aerial then you should get the HD mux OK!
Argos typically exclude such products from their 'no questions asked' returns policy.
Borrowing a box from a friend or neighbour to check reception would be worthwhile.
An aerial upgrade is very unlikely to be needed if you can get SD Freeview. The system used, DVB-T2, I find is more robust than DVB-T, used by the SD services and most transmitter sites are broadcasting all the PSB muxes on the same power.
Much of course will depend on the sensitivity of the box - if you just want an HD tuner that will access BBC iPlayer, look out for the refurbished Technika STBHDIS2010 from the Tesco Outlet on eBay. They often release a batch between 9 and 10 am on Mondays and are under £30 including p&p.
One advantage of buying on line is that you are covered by the Distance Selling Regulations which entitles you to return the item for a full refund within 7 days for any reason (Argos's terms and conditions are illegal under this and they cannot refuse a refund for mail order items however they are one of the most expensive high street retailers - if you want anything other than a simple tuner + iPlayer, get it from Richer Sounds.)