In the UK every party does things differently, but being a member of a political party gives you the right to vote in the selection of candidates* for local government and Parliament, and the opportunity to join internal party organisations and networks that will give you an input into policy-making.
*There is no process for public registration for the public electoral authorities to conduct primaries.
Once upon a time, policy formulation was done very differently in the different parties- essentially, in the Tories the parliamentary party and its leadership set the policies and plans, though there would be various influential specialist groups arguing for different ideas and approaches - input from the bulk of members through their local constituency associations and the national party conferences was fairly indirect. As far as I know, things haven’t changed that much, since this year’s much-criticised manifesto for the general election seems to have been drawn up by the leader and a very small group of her coterie.
In the Labour Party, the process used to be much more public, with members in the constituency parties, as well as the trades unions, putting forward motions to the national party conferences, which could lead to long-drawn-out meetings trying to “composite” motions to get to a compromise/consensus, and for quite a while some knock-em-down debates at party conferences, especially over issues like nuclear weapons. For decades there was a tug-of-war between the parliamentary party and the (usually more leftwing) activists in the constituencies, and always with the risk that the conference would be bounced into passing resolutions that would be seized on by the press as “loony left”, even if the leadership was able to keep them out of the election manifesto - but then the conference rows with the leftwing activists would be reignited. Or they did make into the manifesto as in 1983 - described as “the longest suicide note in history”. It was feared that the election of Corbyn was a revival of all that, though the election result has rather taken the wind out of the critics’ sails.
It was in reaction to the internecine warfare within the Labour Party of the late 70s and early 80s that the breakaway SDP was formed, and from the outset, they instituted a “National Policy Forum”, in which constituencies elected people to work as a sort of internal parliament on developing and updating policies in a more organised and considered way, a process that, AFAIK, also applied in the old Liberal Party and in the merged Liberal Democrats.
As I understand it something similar developed in the Labour Party under Blair. Certainly, the main sessions of national party conferences held in the autumn of each year tend now to be booster rallies for cheering the leadership (as they always tended to be for the Tories), with any policy debates going on in fringe meetings and behind closed doors in internal party committees and organisations.
AFAIK all parties will have some provision for refusing membership, or expulsion, where someone is actively supporting another party’s candidate in an election, or behaves in a way that contradicts what they’re committed to in a party’s declared statement of values (as distinct from particular policy ideas), or otherwise “brings the party into disrepute”. Some people in civil service jobs at or above a particular level of seniority are not allowed actively to engage in party politics.