Yes, but you cannot bring large bags like luggage. Also, please note that for security reasons bag searches will take place at both Westminster Abbey and the Houses of Parliament. The following items are not allowed inside the houses of Parliament:
Sharp items e.g. knives (including Swiss army knives) scissors, cutlery and screwdrivers
Paint spray
Padlocks, chains and climbing gear
Items that make a noise (e.g. whistles)
Banners, placards and flags
Liquids that are not in sealable containers
Please do not bring them. If you have them confiscated from you upon entering, Walks cannot be held liable for the loss of your posessions.