I think you are confusing single responsibility with interface segregation.
From the client/service interface perspective, you should keep your contracts lean and mean. See below for an example of that.
On the SRP side of things, that should be entirely internal to the service implementation and the client should not be aware of this. If you service code is too large, split it up into classes. Then have your service code, at least initially, act as a facade and forward all the calls to the relevant objects. Later on, you have the option of spliting your service into multiple services. But be aware, that SOA and object oriented design, although overlap, are separate and have different requirements.
Interface segregation example: We have a service here at work that we use to do various functions on some business objects. The original service had one interface. As it grew, we realized we had three family of methods: data object persistence, business updates, business analysis. We split up into three contracts. Our client/service implements all 3, so the only thing we had to do was split the contract into three and setup two additional endpoints in our WCF configuration. Very simple.
Hope this helps.