Note to readers: The OP has stated in the question that they and their potential employer is "keen to make this cooperation happen", and believes that the main hurdle lies in getting a Tier 2 visa. This answer is tailored to this assumption accordingly.
The advice is to first clarify with your potential employer's contact if this is the case, as the delay could be due to bureaucracy within the employing organisation (i.e. nothing to do with visa). In this case, assuming you are sure the company really, really wants you, chase up as frequently as you can.
What time-interval would be normal to send follow up email in this situation?
There are a number of hurdles that an employer has to go through before you are allowed to apply for a Tier 2 visa. Each stage takes a different length of time, and in some stages you should not expect an updated response for weeks. Thus an obvious thing to do is to clarify with your potential employer which stage they are in regarding the process, and adjust the contact frequency accordingly.
This involve a lot of information but I will try to keep it short - there are four main stages an employer has to go through from scratch. Not every employer starts from scratch though:
Becoming a sponsor: In order for the company to sponsor you, they have to either:
a) apply for a sponsor licence if they had not done so. There is no upper time limit on how long it takes if the case is complicated, but usually it takes the time it takes to get the documents ready - 1-2 weeks, plus the time it spent with UKVI - around 8 weeks:
Most applications (8 out of 10) are dealt with in less than 8 weeks. UKVI may need to visit your business.
b) fulfilling an action plan to become an A-rated sponsor again if they are downgraded to a B-rated sponsor recently (up to 3 months).
Conducting a resident labour market test, if required. This takes at least 28 days, though it can be done before they decided to hire you if done in the right format.
How long to advertise the job for
You must advertise in the UK for at least 28 days. This can be continuous or in 2 stages.
Be allocated a certificate of sponsorship (CoS). This can take:
a) No time at all, if your employer got some unassigned unrestricted CoS with them.
b) Until the next allocation meeting for restricted CoS. The committee in question meets every month, rank every sound application in descending number of points in their system, and approve them until the monthly quota is reached.
c) A few months, if an application is not sound, or does not meet the cut off in successive allocation meetings. The cut off for October and November allocation is 21 points, and the recorded historic high is 60 points (which occurred in June 2018 and led to some news coverage along the way), so it should not be a huge concern for the OP, who stated they got 80 points.
Assigning the CoS to the worker. This has a 3 month limit once the CoS is allocated:
Certificates must be used within 3 months from when they’re assigned.
In practice this should be done in a week or two.
The information above is extracted from this 202 page Tier 2/5 Sponsor Guidance from UK Home Office, plus various GOV.UK website when linked. Here a sponsor refers to an employer who "sponsors" one to work in the UK.
