I tried to Google search terms "walked from greece tp uk asylum syria" but no matching story came up. Not even from ITV website.
Among the results, though, This story, from March, was about UK quietly turning Syrians away but the numbers involved are only in the tens.
It then goes into one case history which begins with a student, in UK when Syria conflict broke out, who has funded all his siblings and his mother here ("family reunification" regs) but his dad was fingerprinted in Italy (boat rescued) and is thus stuck there. "Uneducated and can't speak Italian… misses his wife of 30 years' marriage". A sorry tale.
http://www.theguardian.com/uk-news/2015/mar/11/syrian-refugees-uk-visa-asylum-seekers-visa
The page also points out that work visas cannot be approved, as long as the country of origin is a war zone because the standard condition of "expectation of return to country of origin" cannot be met, within reason.
Thus work visa/asylum are mutually exclusive things.