OK, I've escaped from picking plums, so back to plumbing! The 22l/m
flow rate corresponds to about a 3-5ft head on 22mm pipe. This tells us
the problem is on the inlet side of the pump, as the flow rate with 3bar
head would be up to 400l/m!!! It is a 22mm inlet size pump isn't it? A
15mm inlet can't cope. It seems as though you are looking for a flow
rate of around 30l/m, which with your head would require at least 28mm
piping into the hot water tank from the loft tank and separately fed
28mm piping from the loft tank into the cold side of the pump. The
problem is probably coming from the hot feed out of the tank being in
22mm with a few bends in the way. A 90 bend corresponds to about 2ft of
piping if in copper and about 5-8 ft if compression. What I would
suggest is that you double up on the Essex flange by adding a Surrey
flange and connecting the two together with 22mm, opening up to 28mm
where they combine keep the bends to a minimum, use street elbows if
possible and feed to the pump in 28mm as far as possible. This on paper
and with a bit of guesswork will give you about 40-50l/m into the pump
which hopefully will be sufficient. I would add however, that if you are
using water at this rate, the chance of a hot shower lasting more than
5-10 minutes is pretty unlikely, also the loft tank will empty, as the
inlet valve almost certainly can't deliver more than 10l/m.

Hope this helps

Regards
Capitol