There are also different lenses for slide projectors, which can make a significant difference in viewing. There are flat field lenses for glass mounted slides, and curved field lenses for cardboard mounted slides. Slides heat up with the amount of light going through them and "pop" a little when projected. Most slide projectors have a design that runs warm air over the slides as they approach the projection slot, so they are "pre-popped" and sharp when they first come up.
There are also zoom and single focal length slide projector lenses, and plastic and glass versions. Zoom lenses are convenient for filling the projection screen without moving the projector back and forth, but a lower grade plastic zoom projector lens can negate any care you take with shooting sharp slides with good lenses. I believe that Kodak has halted slide projector production, but some others still make them. A good used unit might be your best bet. I'd recommend a non-zoom glass lens. There seem to be plenty about if you keep your eyes open. I bought a nice Kodak with a fixed focal length glass lens for my son for US$5 at an estate sale.
Institutions are also phasing out slide projectors in favor of digital projectors. You might contact local audio visual departments at local schools or businesses to see if they'd sell. Apparently listening to someone read bulleted Powerpoint lists of talking points has made slide projectors "obsolete". I have a dozen slide trays that came from a local community college when they put all their film slides onto Powerpoint presentations on CD-ROM.
Rear projection desktop viewers have never been very popular here in the US except for small audience business presentations, so I haven't seen many. The inexpensive small tabletop viewers for individuals often have magnifying lenses that have too much distortion and too many aberrations for critical viewing. That would most likely include the Jessops and Reflecta viewers you linked to. They are not at all like a nice large image projected with a good lens. You could make your own small rear projection screen and use that with a regular projector.
I see the Reflecta slide projectors at Amazon.uk, but have no experience with them. Wish I had more experience with the history of UK offerings so that I could be of more help in pointing you at something used.
Lee