I have an issue with Google Analytics that I need resolving.

General information for the website: We use the website to rent out our holiday cottages.
Kind of development: Customization of existing website
Description of requirements/features: BACKGROUND
On the website www.high-grange.co.uk (created using square space) we use an external booking engine (Free 2 Book)
When customers go to check availability they are sent to Free 2 Book.

We want to monitor which referrers are generating inquiries and sales - events are recorded by the booking engine and we record these as conversions using Google Analytics.

PROBLEM TO BE SOLVED:
* Traffic referred directly to the booking engine (for example from here http://www.iknow-yorkshire.co.uk/accommodation/466-high_grange_cottages_-_bedale.htm) records the events correctly listing the referrer.

BUT

Traffic referred to the home page high-grange.co.uk (like from this site http://where2walk.co.uk/yorkshire-dales-accommodation/cottages/attachment/high-grange-cottages/) records the referrer correctly but when the customer moves over to the booking engine the source/medium for the event is recorded as (direct) / (none).

I imagine this is a simple job but I can't figure it out with my limited knowledge and need referrals to be recorded correctly to measure which marketing is successfully creating leads and bookings.
Extra notes: This is the code that i am currently injecting across the site:




(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','//www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-39207055-3', 'auto', {'allowLinker': true});
ga('require', 'linker');
ga('linker:autoLink', ['freetobook.com'],false,true);
ga('send', 'pageview');