Improper grounding can account for a lot of problems such as you describe. I can answer for the US case; I don't know where you are, but the term "earth" makes me think UK, or certainly non-US. UK is probably similar but with different terminology. The EC has a number of ways of designating grounding schemes such as TT and TN, and the scheme in use at your installation would determine the final answer to your question.
In NEC (National Electrical Code, US) installations the answer depends on the type of ATS, that is, whether the ATS is 3-pole (solid neutral), or a 4-pole (switched neutral).
By the National Electrical Code, if you are using a 3-pole ATS, then you must have a solid neutral and must ground the generator frame through the service equipment (i.e., o/c device used to terminate the utility connection--I don't know the UK term). Do not drive a separate rod at the generator in this case.
On the other hand, if you are switching the neutral with a 4-pole ATS, then you need a separate ground rod at the generator. Although the NEC handbook diagram (Figure 250.7) does not show one, you will also have a separate service disconnect for the generator ahead of the ATS (usually the generator CB), unless the ATS is service-rated (it will have a CB in the cabinet). In the US, service equipment must have a label on it that says that's what it is.
The advantage of the switched neutral is that you can use a GFP scheme when on backup power. With the s/n, you only get GFP on utility, because the main bonding jumper is at the service equipment, which is switched out on backup.
Wm