Hello,

I was just wondering if 175/70R13's fit on my 6x13 wheels and 7x13's wheels or will I need to buy different size tyres

Thanks
Liam

Our English cousins might disagree, but I think 175s on 7" rims is too narrow to be safe.  175s on 6" rims would be OK, but I wouldn't want them any skinnier myself.
 
Check out this page put out by Yokohama for an idea of what's what:
 
http://www.yokohamatire.c...izing/rim_wheel_width/

175/70 will go on both wheels easily, legally the 175 should not be on a 7" rim.
but they are hardly a stretch if that is what you are after.
 

 
(excuse the tread depth, fun was had)
 
the only other option inside that ball park is a 185/60 which are getting harder to find. 
 
as far as the 'safe' option a 205/60 is what would be recommended by 90% of tyre fitters