The cartridge on the turntable puts out a very small signal (about 0,1-3mV), the normal input (cd, tuner, tape, aux) on an Amplifier needs a Larger signal (0.5-2v) so inbetween the turntable and the amp there needs to be an additional amplification stage. This amplification stage can either be in the turntable, a separate box or built into an integrated amplifier (phono input).
The A1 has an aux/phono input, iirc in most cases this is an aux input requiring the hire voltage output sources (cd, tuner, tape etc.) but there was a dealer fit board that converted this to a phono for use with turntables.
I suspect given your explanation that the deal fit phono board is not fitted so you will need an extra box to increase the signal from the turntable. these can be had from £25 to £25000.
The first check would be to let us know what turntable you have to double check it does not have a preamp fitted in that. Then let us have budget and I am sure there will be suggestions.
Examples below would work.
Amazon product ASIN B000H2BC4E
Amazon product ASIN B01NCVTR7V
Amazon product ASIN B07NCYJ1PR
These can all be had second hand cheaper if you are ok with buying that way.
Finally, as you suggested you could change the A1 for a different integrated amplifier but that will be a bigger expense so will need to understand budget, speakers you are using, other sources etc.
Hope this helps.