Westminster’s second chamber now has more than 800 peers compared to the 650 MPs in the Commons, making it the second largest legislative chamber in the world after China’s People’s Congress.
A report last year recommended its size should be cut by a quarter over the next ten years and new peers should be limited to a 15-year term.
But Mr Sheppard, MP for Edinburgh East, said 2018 was the “last chance saloon” for the Lords and claimed the modest attempts at reform set out in the Fowler report already looked timid and limited.
He said: “2017 was a year of potential opportunity for reform of the House of Lords.
“So desperate are things that last year’s reform was attempted, not because of any motion or suggestion from an elected Member of the House of Commons, but because the House of Lords is asking us to take action to try to salvage its credibility and reform the institution.
“The recent Fowler Report on the House of Lords may have been the last possible chance for reform. That opportunity may now have been missed.
“Peers are not accountable to the electorate and the chamber is now stuffed with party hacks, cronies and election losing has-beens, as well as convicted criminals. It is an utter affront to democracy.
“We are fast approaching a situation where the legitimacy and credibility of the House of Lords will be in crisis.
“The reforms suggested in the report were too limited and timid.
“We cannot be in the same situation this time next year the window for reform is closing. We must now look and prepare for the complete abolition and replacement of the Lords.”
Mr Sheppard, who is the SNP’s spokesman on the Lords, said the second chamber was “staggeringly unrepresentative” of the population at large, with only 26 per cent of its members women; 44 per cent living in London and the south-east of England; and 56 per cent over 70.
He said: “That is an institution that in no way reflects society. It is also an expensive institution, costing almost £100 million for every year that it operates, £20 million of which goes on the expenses and stipends of the members who serve in that Chamber.”
Peers can claim a £300-a-day attendance allowance plus travel costs. Last year 455 peers claimed more than the average UK salary in allowances alone, even though the House of Lords only sat for 141 days.
And £1.3 million of the total claimed went to 115 lords who did not speak once.
A recent Electoral Reform Society found only ten per cent support for the House of Lords remaining unchanged as it is today and 62 per cent saying the second chamber should be elected.