Dee
Your Local Authority should be aware of what you receive for ESA already but it can do no harm to check.
Whilst Housing Benefit is a means tested benefit the amount you are entitled to is calculated differently from your ESA. Basically you have an allowance based on your circumstances and housing needs, as long as you are entitled to Income Related ESA, which you are from your post, then you receive the full allowance, your starting to receive the premiums will not increase it.
If you are paying £38/week then this will be because your actual rent is more than the Housing Benefit payable for your property.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems