Thank you very much! I would like you to check these few more statements, too.

1) Summarise briefly (or briefly summarise) the history of England from the prehistory (or from its prehistoric inhabitants) to the Anglo-Saxon invasion (or to the Anglo-Saxon invaders)
2)His cousin suggested he should apply (he apply is also correct?) for a job at his agency, he accepted and was eventually taken on (?)
3) He believes that in his new job a lot of the writing is like writing poetry but the work environment is completely different.
4) Actually, it is more competitive and sometimes there is quite a lot of jealousy and resentment, especially if you are successful.ù

Thank you a lot

1) Summarise briefly (or briefly summarise) the history of England from the prehistory (or from its prehistoric inhabitants) to the Anglo-Saxon invasion (or to the Anglo-Saxon invaders)

Summarise = summarize. You could say it either way. I prefer the Briefly summarize....: Briefly summarize the history of England from its prehistoric inhabitants to the Anglo-saxon invasion.

2)His cousin suggested he should apply (he apply is also correct?) for a job at his agency, he accepted and was eventually taken on (?)

His cousin suggested that he should apply for a job at his agency. He accepted this and was taken in by them.

3) He believes that in his new job a lot of the writing is like writing poetry but the work environment is completely different.

He belives that in his new job there is a lot of writing which looks similar to poetry, but the work envronment is completely different.

4) Actually, it is more competitive and sometimes there is quite a lot of jealousy and resentment, especially if you are successful.ù

This sentence you may want to change a bit.

you could add one more thing to this sentence:

His cousin suggested that he should apply for a job at his agency. He accepted this and was taken in by them.

OR

His cousin suggested to him, that he should go and apply for a job at his agency. He accepted this and was taken in by them.

1) To summarize the history of England from prehistory to the Anglo-Saxon invasion, you can start by mentioning that prehistoric inhabitants inhabited the land that is now England. Then, you can explain how several different cultures, including the Celts, Romans, and Anglo-Saxons, influenced England during different periods. The Anglo-Saxon invasion marked a significant moment in history when the Anglo-Saxons migrated to England and established kingdoms.

To find more detailed information about each stage in England's history, you can refer to reputable historical sources, such as history books, academic articles, or reliable websites dedicated to English history. These sources will provide you with a chronological overview of England's history, allowing you to summarize it accurately.

2) In the given sentence, "His cousin suggested he should apply for a job at his agency, he accepted, and was eventually taken on." The use of "he apply" is not correct. The correct phrasing would be, "His cousin suggested he apply for a job at his agency." This form is called the subjunctive mood, and it is used to express a recommendation or suggestion. The sentence continues correctly with "he accepted and was eventually taken on," indicating that he agreed to apply for the job and was eventually hired by the agency.

3) The sentence "He believes that in his new job a lot of the writing is like writing poetry but the work environment is completely different" is grammatically correct. It conveys that the person believes the writing tasks in their new job resemble poetry in some way. However, they also note that the work environment differs significantly from what they expected.

4) The sentence "Actually, it is more competitive, and sometimes there is quite a lot of jealousy and resentment, especially if you are successful" is grammatically correct. It reveals that, in the speaker's experience, their new job is more competitive than anticipated, and it often involves feelings of jealousy and resentment among colleagues, particularly if someone achieves success.

If you need further clarification or information on any specific part of these statements, feel free to ask!