Maybe someone who actually teaches English language can do better, but mistakes I can see are :
Imaginary Minister: That is matter for them.
That is
a matter for them.
Imaginary Minster: Investigations are being undertaken by ...
Replace statuary with statutory.
Imaginary Minister: We support the meditation work of ...
Meditation work? Possibly mediation instead?
If it is, I would write:-
... and
we need to emphasise to all ...
Imaginary Member D: Can the Minister tell us ...
Can the Minister tell us what the waiting times are for DLA?
Imaginary Minister: As your Lordship's House ...
The sentence is wrong but I'm not sure what you're trying to say to correct it.