Elly - it's vastly more of a problem because poor children are much more significantly under represented in grammars than they are in even the best comprehensives.
Re: fair banding - yes, this isn't completely problem free. In order to use this method year 6 pupils need to sit a fair banding test. Any part of the admissions process which requires a test will discriminate against the poorest and most disadvantaged pupils, as parents from this group are 1. less likely to realise that the school actually requires this for admissions purposes and 2. even if they are aware they are less likely to bring their children to the school for testing.
Never the less, it still helps. There are probably ways of tinkering with it, for example, having the test sat in local primaries, which would improve this.
By way of example, two of the most successful London comprehensive schools in areas where a family home nearby is likely to cost 600K plus - Dunraven in Streatham, and Harris City Crystal Palace, which is about 4 miles from Dunraven. Both schools are outstanding OFSTED rating and hugely oversubscribed. Harris CP is the only comprehensive to have achieved a perfect OFSTED and is the most oversubscribed comprehensive in the UK.
Their FSM figures are
Dunraven: 18.8%
Harris City: 9.8%
By comparison the national average rates of FSM at grammars is less than 3%.
And I'd say that Harris City's FSM rate is unusually low.
My dc's comprehensive (where most nearby houses are in the £2 million mark) is very successful - 79% 5 A-C's including maths and English. It's hugely oversubscribed. 28% of dc's there are on FSM.