Without doubt London is sadly lacking in reasonably priced, convenient helicopter access both centrally and peripherally.
Battersea is out for most of us small operators since the price hike and there is no London HLS within walking distance of public transport links.
This is shameful for such a great capital and a real opportunity exists here to improve the situation and hopefully start a financially viable business.
IMHO there are 2 options.
1.The plan you outlined above - central would be nice for pilots and pax but as you can see above even those involved in aviation don't want it around them all the time.(They can often be the most vociferous complainers!)
2.Find a site directly adjacent (walking distance) to a good fast (less than 30mins) rail/tube link into central London. This does not exist at present - taxis between landing site and train should not be necessary and spoil the flow of the trip in and out as well as adding cost. This could even be a grass field with a windsock (no need to buy a ship and pay through the nose for maintenance / mooring) plus you end up with an appreciating investment rather than a deprecaiting hulk in the Thames with a huge noise lobby against you.
You find the site and I'll go halves with you!
SB