The vent would never be after the circulator
unless the circulator was on the return side of the boiler and that would be bad practice (it was common 50 years ago for other reasons).
On a modern system having the vent after the pump would be non compliant, the vent must always connect to the boiler flow pipe side.
BS6798 states....
5.4.1 Open systems
For open systems, an open vent pipe shall be provided from the circulating system to discharge over the feed and expansion cistern above the level of the overflow connection. The internal diameter of the pipe
shall be not less than 19 mm. The vent pipe shall rise continuously and be connected in such a position as to prevent discharge of water or ingress of air in all normal conditions of service. There shall be no valves
or components other than full-bore pipe fittings between the boiler and the discharge point of the open vent pipe unless specified in the manufacturer’s instructions.
COMMENTARY AND RECOMMENDATIONS ON 5.4.1
Except where the boiler manufacturer’s instructions specifically state otherwise, the open vent pipe should be fitted to the flow connection or flow pipe from the boiler. The vent pipe may be used as part of the
circulating system. Except where the boiler manufacturer’s instructions specifically state otherwise, a close coupled cold feed and open vent configuration may be fitted provided that there is a cold water feed path
available when all automatic valves are in the closed position. When this configuration is used the cold feed and open vent connections should be not more than 150 mm apart. Except where the boiler manufacturer’s
instructions specifically state otherwise, a combined feed and vent pipe may be fitted provided that the boiler incorporates an overheat cut-off device.
The vent is always the first connection on the flow pipe and modern practice and regulations dictates the feed pipe will connect after it and within 150mm. As mentioned before this short length of pipe is effectively operating as the neutral point through its entirety by virtue of the minimal head loss (the water flow friction between the connections is negligible and hence no pressure difference)...the pressure here remains at the same static pressure with the pump on or off.
Provided the boiler manufacturer allows the vent and feed pipe can be combined into a single pipe however IMHO it's poor practice and venting can be slow. Like all corner cutting in the building trade it was no doubt done under pressure to reduce costs in the new build market (new build installs can be dire).
Connecting the pump after the close coupled Feed & Vent ensures the negative inlet side of the pump operates close too or a little below the static system pressure (the neutral point pressure). How far below depends on the head loss (pipe friction) between the close coupled F & V and pump.
This layout has the advantage of maximising the pressure around the radiator/cylinder circuit (the positive pump pressure is added to the static pressure) at the pump outlet side and in so doing helps to reduce air ingress through radiator valve stems etc.
If you take a look at sealed systems the expansion vessel connection to the system equates to the neutral point and you can almost guarantee that on any modern boiler it will also be on the inlet side of the pump whether that be a combi/system boiler or a heat only boiler layout diagram. Again it's to maximum the positive pressure to the system (and the heat exchanger in the vast majority of combi/system boilers...it also aids bleeding).
150 years of heating has arrived at this situation but if you've got an old system then all manor of configurations have been used, even as little as 20 years ago 4 pipe heat exchangers were available with feed/vent/flow/returns etc.
If you want to understand the close coupled F&V being limited to 150mm take a look at Primary/Secondary systems (aka Closely Spaced Tees) more widely used in the US.
An enhancement to that are Low Loss Headers and Buffers used here on large systems.