Is there a digi box that can connect to a TV without a scart socket?

My mums TV is that old, I remember when it was new in 1985! but it has no scart socket. I was thinking we could connect up the tele through the aerial socket to an output aerial socket on a digi box, much like video recorders used to hook up. Then all she needs to do is tune the tele to the digi box and use the digi box remote to change channels…

I've got a portable without SCART, will need something like this:
http://www.argos.co.uk/static/Product/partNumber/5321375/Trail/searchtext%3EFREEVIEW.htm
if they ever switch off analogue signals in my area.

Buy her a new TV with freeview built in.

I bought my parents one of those TVonics MFR-200 units, it works well. Is the same programme guide, remote, etc as my virgin freeview box, think they're made by the same people.