One option is Rom Yen Spa in Malden Road, NW5 in the Gospel Oak area. I haven't been there but it might be worth a look. Not strictly in Islington but Gospel Oak overground station 10 minutes walk away down Mansfield Road is connected to a number of stops in various parts of Islington (Caledonian Road, Highbury and Islington, Canonbury, etc.), none of which is more than a few minutes away from Gospel Oak once you board the train. As far as I know nobody on here has yet reported on it and it remains terra incognita.