NAME THAT CONIFER

Can any of you naturalists tell me what this lovely tree is? It's a huge old conifer at Mount Grace Priory where we went for an outing this morning, and it's covered with these red flowers / conelets / whatever-they-are.

Edit: Consensus on another website is that it's Lawson Cypress.

A good morning followed by a very underwhelming pub lunch and a lacklustre afternoon. I may have an early night and reset myself for tomorrow!