It used to be suggested that Roger Mortimer, Earl of March, was nominated as Richard II’s successor in the Parliament of 1385, but this was questioned by historians due to lack of supporting evidence.
It appears that March was in fact so nominated in the Parliament of 1386. (Source – (Ian Mortimer, ‘Richard II and the Succession to the Crown’, History, vol. 91 (2006), pp. 320–36.) This explains why the Westminster Chronicle (written in the 1390s) is quite clear that March, not Lancaster, was heir.
The Parliament of 1386 – the Wonderful Parliament – busied itself by being extremely critical of Richard’s government. It impeached the Chancellor (the Earl of Suffolk) and caused the removal from office of the Treasurer. It also set up a Commission which pretty much took over the government for 12 months. So in other words “the opposition” was in charge. This may explain why the Mortimers were not elevated in any way, because Richard II may not have approved of the nomination. Of course only he, personally, could give promotion within the peerage or in terms of precedence. There is no suggestion that March ever took precedence of the dukes of Lancaster, York and Gloucester. Indeed, from what I can make out he had only the precedence due to him as Earl of March and nothing more.
Late in Richard’s reign March fell from favour – just before he, March, died. Ian Mortimer has stated that he believes Richard intended Edmund of Langley to succeed him at this point, and this seems likely given the alternatives.
It is worth noting that no “rules” governing the succession were in place at this time, and in the absence of a direct heir it was not absolutely clear who had the right to determine the succession. The King? Parliament? However the very fact that the 1386 Parliament felt competent to make this determination suggests strongly that even this early in history the role of Parliament was decisive. Had Richard reigned longer, would he have produced a succession statute, or Letters Patent to determine the matter? Sadly, we can only speculate.