He alleges [that] another million pounds had gone on material purchases based on projections of Arcadia orders [that] he was told were coming down the line.
This sentence is not simple at all. We should be able to count the finite verbs to discover the number of clauses involved.
He alleges 1 another £1m had 2 gone on material purchases based on projections of Arcadia orders he was 3 told were 4 coming down the line.
There are four clauses. Not only do we have a clause within another clause, we have clauses nested three levels deep.
The outermost matrix clause has the subject/verb pairing he/alleges. The rest of the sentence is the direct object of this clause.
This direct object is a content clause, also called a nominative clause. This clause could have been introduced by the word "that". We also might call this a contact clause, since the optional introductory "that" doesn't appear in the original example. We generally regard a subordinating "that" to be optional when it doesn't represent the subject of its clause. The subject/verb pairing of this clause is pounds/had.
The next clause we encounter in this sentence has the subject/verb pairing he/was. This, too, is a contact clause, with it's optional "that" left unwritten. Instead of a content clause, this is a relative clause. The entire clause "[that] he was told were coming down the line" modifies the noun phrase "Arcadia orders".
Finally, we find a clause with a subject/verb pairing that is quite difficult to see. The subject of the verb "were" is missing, or at least it is far from obvious.
The subject of this clause happens to be the same "that" which doesn't appear in the matrix clause that contains it.
Arcadia orders were coming down the line.
The original sentence does not tell us whether this statement is true or false. Regardless of the statement's truth value, it is something that was mentioned:
He was told [that] Arcadia orders were coming down the line.
In this example, "Arcadia orders" serves as the subject of the verb phrase "were coming", and the subject/verb pairing orders/were is easy to find. The "that" which introduces this thing which was told is optional.
. . . projections of Arcadia orders [that] he was told were coming down the line.
Here, we have an oddity. The "that" which is optional for the clause he/was is also the subject of the clause [that]/were. We're looking at projections of Arcadia orders -- the same Arcadia orders that he was told were coming down the line.
Your original example is not a simple sentence. It is a complex sentence. It is, in fact, a deeply complex sentence, containing three levels of nesting. A content clause is contained within a relative clause which is itself contained somewhere in another content clause.
It is also a very complicated sentence. The connectors that you hoped to see are invisible. Their existence is merely suggested by the positions of the clauses to which they would apply if they were not left unwritten.
Arcadia orders might have been coming down the line. Someone was told that they were. Another million pounds might have gone on that basis. Someone alleges that they had.