New member - letting agent contract issue and fee increase notice

Letting Agents

Hello,

I'm relatively new to becoming a landlord and have already hit a couple of bumps in the road.

Being new I instructed a letting agent to give full management of the property - letting agent was recommended to me by my FA.

Tenant is in the property and AST all done - no issues with that...

BUT...

Despite asking 4-5 times for the letting agents terms and contract between them and myself (landlord/letting agent contract) I have only been sent a price list of their fees and told to sign and return. My initial question is - surely this cannot be right? Shouldn't I have a contract with them stating basics like how much notice either party has to give of any changes including fee changes and terminations etc? I assume the letting agent should be supplying this or is it something I am meant to draw up and get them to sign? 

Last week I was told their fees for management is rising as of 1st May (less than 1/2 a month away). Is there any law in place about giving notice of such changes as surely half a months notice of an increase isn't enough? 

Thanks in advance for any help with this.