Every now and again I hear this bird in various places around the village and surrounding area. I have tried to record it but it’s often just too distant. It’s sounds like “phar-ooh” almost a purr with a subtle bird song note. I can’t imitate it either . And I’ve yet to spot it.
Well without a recording or a photo people are going to struggle. My best advice would be to go to the RSPB site, or Xeno-canto.org and listen to pigeon and dove calls which is all your description brings to mind.
Also 'the village'; there are lots in the UK, it's helpful to know which village/county.