Mixer or Eliminator

[Tonedeaf]

I am trying to get a simple karaoke setup for the wife and her friends.
They are very much untrained, amateur karaoke singers.
Definitely not a singer myself but I will be going it a go too on occasion.
This is just to be a cheap system, for now so I am not expecting great things..
We will spend more when finances allow it, if it is something that takes off with them (I think it will).
The music will come from the TV to begin with. Just karaoke channels from YouTube
I have an ION Block Rocker Plus speaker for the vocals.
I have a UHF microphone system with dual mics. Bought from Amazon for about £60.
This will be used in a small room, under 7m X 4M.
The TV and speaker are next to each other at one end of the rooms length.
The mic system is right above the speaker.
They will be singing about 2-4 meters from the speaker.
I have been giving this a small test. Changing volume levels on the speaker and the mic system.
The level of feedback is very alarming. Mostly low sounds but some high pitched too.
Only having the volume really low and the singer being 4+ metres from the speaker stops it. And then not completely. The room size just does not allow this.
I have looked at guides online for how to fix this and taken the suggestions in (mic close to mouth, don't point mic at speaker, don't cup mic etc).
Any other suggestions just are not practical to implement (moving speaker further away, soft wall coverings etc).
This has not really helped a great deal and controlling other peoples use of the mic is not easy.

I have had it suggested to me to get a mixer and/or a feedback eliminator.
Would this work effectivly and if so any suggestions for model.
Price is a big factor. Definitely needs to be under £100.

Thanks.

[Val]

I am not aware of the gear that you have.
It's very difficult to create a home karaoke set-up.
What with acoustics and feedback etc.
I could never find an effective feedback eliminator so I never tried setting up at home.
Mind you my systems are powerful.