Sorry I ran out of steam yesterday and needed to go to sleep. Here are some quick answers to your questions as I see it
There has been a lot of talk about saving money in the NHS really since the 1980's and there have been various attempts to make this "more efficient" by introducing managers and the introduction of NICE under the Blair government ...its main purpose being to save money on treatments. The part that appears to be privatised are the ancillary services and represent less than 10% of the total NHS revenue. The concern raised by many are that this is growing and the tax payer doesn't seem to be getting the best deal vs having these services in house and more efficient (like having electronic records that are transferable between departments etc.). The following explains it better than me
https://fullfact.org/health/how-much-more-nhs-spending-private-providers/
All medicines have to get NICE approval and NICE are about saving money on effective treatment not wheeling and dealing and taking bribes from pharmaceuticals. Perhaps that is going on, but where would they hide this bribe money? I think this is something that may happen in private healthcare, but as I've said previously the NHS isn't private.
I think the department of trade (or whatever its called now) may do deals for manufacturing in the UK with large pharmaceuticals but this is unlikely to concern individual treatment options.
The main saving though, is making sure people don't get sick or sicker and cause more expense later on as they "block beds" and need expensive operations because they weren't vaccinated or whatever. I think this has been answered more eloquently elsewhere though.
So in the case of homeopathy, this won't get past NICE approval because there is no evidence that it works more than placebo/bias. So if there is no proof that the treatment works, there is no cost saving as a treatment that will prevent further expense.
In fact it will cost the tax payer since it will need to be funded with trained and approved practitioners and presumably need regulation somewhere as well. This all would mean that the NHS budget would have to be cut somewhere else to fund it. The budget has been cut now to such an extent that some local authorities are removing fertility treatment for patients.
That has nothing to do with pharmaceuticals blocking it's use.