Bit risky sticking my head above the parapet after my last fail, but:-
Is this because the approach plate for that airport says you must do so or because ATC require you to? (HD jumped in before me: it must be a traffic-management issue, too.)
A bit of both in practice. Some of the Jeppeson booklets state minimum distances to intercept final approach and in other cases ATC will advise this when clearing you for a visual approach.
Regulations will be in the AIP. Here's an extract of LGW's AIP:-
2. .
a. Except where sub-paragraph (12) (b) applies, the aircraft shall not join the final approach to either runway at a height of less than 1500 ft aal
b. where the aircraft is a propeller driven aircraft whose MTWA does not exceed 5700 kg, it shall not join the final approach to either runway at the aerodrome at a height of less than 1000 ft aal and shall follow a descent path which will not result in its being at any time lower than the height of the approach path normally indicated by the PAPI.
13. .
a. Where the aircraft is using the ILS in IMC or VMC it shall not descend below 2000 ft (Gatwick QNH) before intercepting the glidepath, nor thereafter fly below the glidepath; and
b. an aircraft approaching without assistance from the ILS shall follow a descent path which will not result in its being at any time lower than the height of the approach path normally indicated by the PAPI
14. Between the hours of 2330(local) and 0600(local), inbound aircraft, whether or not making use of the ILS localizer and irrespective of weight or type of approach, shall not join the centre-line below 3,000 ft (Gatwick QNH) closer than 10 nm from touchdown.
I am struggling to understand the relationship between an approach procedure/plate and a visual approach. Am I correct in thinking that a visual approach allows you to 'short-cut' part of the approach procedure?
A visual approach allows you to visually manoeuvre to a landing. This may involve joining downwind, base or a simple straight in approach.
Except for local regulation such as the Noise Abatement requirements there is no need to carryout any part of the instrument approach procedure.
In a non-precision approach, you have to be at specific altitudes at specific points, right? But if it is also a visual approach, do those requirements not apply? I don't see how you can have both
No they don't. These minimum height requirements are there to stop you hitting terrain when in IMC. They don't apply when doing a visual approach.