how can I fix TV as it only works when I touch the aerial plug into tv?

just gone digital.
Tv (new Sony)works fine on analogue but is marginal on digital. sometimes I get a picture (normally daytime) sometimes I don't.
However if I touch the metal aerial plug where it enters tv picture is fine.
Landlord says aerial is ok and will charge me £100 if I call aerial fiters out and it is not the aerial.

Any suggestions, please?