SQLCLR isn't really meant for this - it's ok for simple functions that are better done in CLR (like needing to run a RegEx on something for example), but even then it creates dependencies and management issues it shouldn't have to (your DBA shouldn't need to know .NET, your .NET developer shouldn't have to be a DBA, etc.).
What you should do here is create an ADO.NET application that consumes the webservice and then passes the relevant data to SQL server, or consumes data from SQL server and passes the relevant data to your web service. You want to keep your web service abstracted from SQL Server and vice versa - don't try to make SQL Server a WCF client (it will do poorly), just give it the data from a well written WCF client.
In other words: let SQL Server handle data and .NET handle WCF.