Hi Kay, from the picture, which isnt totally clear, I would say it was a Chamaecyparis lawsoniana (Lawsons Cypress) Before C. leyandii took over as the main screening conifer, these were widely planted but there was one draw back, they were grown from seed, which meant you had alot of variation in type. The reason that I'm telling you this is so that you understand that it could be tall and thin, wide, slightly weeping but that aside, it will grow quite large at a rate of 60cm. a year. It lends itself to being trimmed but only as far back as the green shoots and will not readily shoot from bare wood.
Lannerman