I have found RJ45 plugs to BT sockets which would allow me to plug a phone
into a RJ45 outlet. But at the panel end I want the opposite a BT plug to
RJ45 socket to fit in the BT socket so I can then patch to the panel. Do
these things exist or is there and easier way to achieve what I want.

At the phone end, I used secondary RJ45-BT socket leads like you have
found. At the phone line end, I used the same, with a male to male phone
plug lead obtained from www.netshop.co.uk.

For the patching, I had a patch panel larger than required for all the
connections. Then I chose 8 patch sockets (all the highest numbers) and
using some stripboard and some cable ensured that the pins were all commoned
together. This allowed short 50cm patch leads to patch a particular RJ45
socket into the phone system, including the one that led to the incoming
phone line. By not hardwiring this, it allowed any socket to configured as a
phone socket (by patching to the commoned area) or a computer socket (by
patching to the hub).

Secondly to connect my broadband router to the patch panel I'd like a RJ11
to RJ45 patch lead. At the moment I'm doing this with a two leads and a
RJ11
to BT coupler connected to a BT to RJ45 coupler.

That should work.

Christian.