Best to go to an aircon specialist. Places like kwik fit ,ATS etc may just be a tyre fitter who had a half day course on using the aircon recharging machine.
Unfortunately in an older car a regas might not last long before it leaks out again. They are meant to check for leaks, but a slow one may be missed. If they find its leaking they cannot legally top it up knowing it will only last for the summer. . It must either be repaired (which may be expensive) or do without air con.
On a more positive note you could try replacing the cabin pollen filter. If its clogged it may reduce the efficiency of the aircon (if its working at all) They are not expensive and may need changing anyway. Its normally an easy DIY job.
IF you decide to go for the groupon ATS offer I'd go for the basic regas, £41.99 The antibac treatment may not be needed ,especially if you change the pollen filter. If you think its necessary Halfords do a diy deodorant/anti bacterial aerosol for £5.99. (and one for £20

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Air from the vents should feel significantly colder if the aircon is working. It also feels 'different' ,dehumidified I suppose. If it only feels slightly colder than ambient thats just the result of being fan blown air.