IMO,although a spacesaver might suffice it doesnt necessarily save that much space. On one parameter ,tread width, it may be 125 mm vs 185mm for a full sized spare. You may only save 60mm/2" less height when its laid down
A spacesaver is only suitable to limp along at reduced speed. A full sized spare would enable you to complete a longer journey at near full speed and take a bit more time finding a suitable and convenient tyre depot . And if the puncture is not repairable, take more time obtaining your choice of tyre rather than whatever they have in stock.
The one on the website at £99 including tools looks a good option but note that it is second hand,although never used. There is a thriving market in used spacesavers some of which may have sat in the boot of a car for many years and susceptible to age cracking. (particularly important as you would already be pushing your luck driving on a narrow wheel) Replacing this with a new spacesaver tyre is comparatively expensive.
In your situation I would try to find a used Jazz alloy that is sold individually and cheap because of kerbing damage. You could try advertisng your requirement for free on one of the spares finder websites.
Or go the whole hog as I did. Obtain a full set of 4 wheels fitted with decent all season winter legal tyres .I fit these in the winter, original wheels in summer. With a winter wheel or summer wheel used as a less than ideal but usable temporary spare, like coldstart.. Sounds daft and expensive, but my winter set have been used on 2 cars so far and has saved me the cost of buying any new summer tyres. (and could eventually sell the set to someone like yourself - sorry not yet ) Also means I can be legal in continental Europe in winter months.