Could be done but not simple or cheap - especially if you want the engine to last, and it still has to pass emissions testing at MOT.
Basically when you turbocharge you need to reduce the compression ratio, the turbocharger makes up the rest. This means mechanically changing the engine (e.g. spacer between block and head or different pistons . . . ) and hence a complete re-map and potentially lots more changes like a bigger radiator, clutch, gearbox, brakes, and for the weight new springs/dampers . . . . . For example VW 2.0FSI has compression ratio of 11.5:1 but the 2.0 Turbo is 10.3:1.
Probably cheaper and easier to look at putting another engine in (e.g. a 1.8T or the new blown 1.4)