My experience was that the first card I got (Vanquis) which started out at £250 limit and crept up in stages to £1500, didn't do a lot ... the agencies saying the low credit limit was a hinderance to a good score. So, after the IVA had cleared. I applied to a Post Office card (£1600, where it has stayed) which helped a bit, but my report still cited low limits as a bad point. Finally, as mentioned before, Co-Op gve me one of theirs with £1000 limit and the warnings regarding low credit dropped off my noddle and Clearscore reports.
Then ... the sticking point was low usage (actually, practically none at all as I was afraid of the things!), so now, I use them, in turn, for petrol and also for big purchases (to get the extra security of the consumer credit act), but still always pay them off before the interest kicks in. So that warning also disappeared. My "score" still isn't perfect, but it is well above the national average and also even further above my local average.
However, as Normanna points out, lenders do not actually see a score, but a usage history (all those green ticks and account limits and balances). They like the confidence that a few lenders have also had the confidence to "lend" and they like to see modest usage against the credit limits (also not too high a total potential lend if you decided to max out the cards).
All a bit of a blindfolded highwire act !
My opinions are merely that .. opinions based on experience. Always seek professional advice.
IVA Completed 23rd July 2013 .... C.C. 10th January 2014