Chaz
Get face to face advice before you make any decisions.
There is no reason why your moving in together will result in your benefits being reassessed.
If your ESA is income based either in part or in whole, then one of you is going to have to surrender their claim, either your ESA(IR) or his Income Support.
If your ESA has a Contribution Based element then this will be treated as income in regard to any Income Related claim such as your boyfriend, so your total income will most definitely not the sun of what you both receive.
Your Housing benefit and Council Tax support may be effected
The advisor you see should be able to calculate what you might receive on the various options.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems