What I did for a while with TD Direct & then ii, was to verify matters via 2 screens. One showing live market prices, the other my trade. When buying, if live market SP ticked up as happened occasionally, & I clicked buy & still managed to get my trade done at SP before the tick-up, to me that was best execution. TDD always achieved that.
My experience with ii was different. Trade would fail if live SP ticked-up a fraction. I’d even check on LSE later. A lot of algo trades made at similar time to my off-book ii trade were at fractionally better SPs.
Net effect: with TD Direct one paid standard £12.50 commission if not trading frequently. But in real terms, it seemed cheaper than that. Obviously, it makes no difference if one is buying lower amounts. It makes a significant difference if frequently buying tranches of 10,000 shares or more.
By the by, one guy on London South-East BBs did a comparison between his 3 brokers: HL, AJ Bell & iWeb. Though iWeb charge only £5 commission, they compared very favourably with the 2 more expensive brokers for execution prices. So cheapness doesn’t have to mean poor service. - Regards.