The area can be closed for a maximum of 28 days per year for shooting, and any closure must be correctly notified (usually at the main access point) and managed by the landowner. If approached by someone representing the estate (unlikely these days as most seem very friendly), state you have a statutory right of access under the CRoW Act, find out the individuals name, and then report the incident to the BMC.
Open access land, designated under the Countryside & Rights of Way Act (2000) give area access rather than linear access as provided by public rights of way. It also gives a legal right of access specifically for climbing, as well as walking and other quiet recreation on foot.
Please bear in mind however that the landowner still has the right to restrict access for up to 28 days per year (often used on public safety grounds for shooting in moorland areas), and can also apply for longer term restrictions with Natural England (such as bans on dogs, or regular restrictions during particular times of year). It is important to check for these restrictions regularly as they can be added at short notice – all details for open access land in England can be found on Natural England’s website.