If you are getting the CDs made professionally (rather than burning off CD-ROMS yourself) the manufacturer will want to see a licence from MCPS. This is straightforward, you give them a list of the songs on the album and they work out the royalties, you pay the fee and they give you the licence. There's a form of words you need to put on the CD label to show it's been licenced. That's all the permission you need (unless, as already pointed out, the song hasn't been recorded before) provided the songwriter is a member of MCPS.

Where a songwriter isn't a member of MCPS it gets more difficult, as MCPS then aren't interested. Then you need to contact the songwriter directly and agree any royalty payment direct with them. Where a song is traditional or out of copyright you don't need permission and don't pay a fee.

I suspect that Morton, Hutchings and Tams are members of MCPS so although they may have given you their blessing you may find that MCPS will still charge a royalty.

If you want to get paid for any airplay you need to register separately with PPL. This protects the rights of the artists (and others involved in the production) in their own performance, so when your album is played on-air or in public you can be paid (the songwriter will be rewarded separately via PRS).

This is for the UK. Other countries have similar rights organisations which no doubt work in a similar way. I believe it's more complicated in the USA where there are several competing rights organisations.