Image source: Getty Images I’m searching for the best cheap UK stocks to buy for my investment portfolio. And the following FTSE 250 shares have recently caught my attention. They’re also among the 10 most popular value shares with investors using Freetrade’s share dealing service. Each trades on a rock-bottom price-to-earnings (P/E) multiple and price-to-book (P/B) ratio. Should investors buy them today? #1: ASOS Freetrade analyst George Sweeney notes that ASOS (LSE: ASC) trades on a forward P/B ratio of 0.6. The online retailer also trades on a higher P/E ratio of 20.5 times, a rating he says could be attractive to value investors. Sweeney notes that “its share price has been in freefall lately” and that investors should “be wary of catching a falling knife.” Yet the company has surged this week after it announced “significant progress” in improving profitability. It’s shuttering office and storage space and pulling underperforming brands to boost its fortunes (the company plans to ditch 35 unprofitable labels in the coming months). These measures could help the ASOS share price rebound strongly. But I still wouldn’t buy the FTSE 250 retailer for my investment portfolio. Sales at constant currencies tanked 6% during the four months to December, to £1.4bn. They could continue to slide too as the cost-of-living crisis endures. Meanwhile, in the longer term it faces increased competition as its rivals improve their own online operations. Demand for its fashion products could also suffer as worries over the environmental impact of ‘fast fashion’ grow. I think the cheapness of ASOS shares reflect these dangers. #2: International Distribution Systems Royal Mail owner International Distribution Systems (LSE: IDS) has also has been popular with Freetrade users. Sweeney notes that the courier “has been getting the attention of many investors as a UK value stock worth a second look.” He notes that the FTSE 250 company “has a P/B ratio of 0.4, a P/E ratio of 9.1 times, and a share price showing signs of recovery after a tough year.” IDS can’t stay out of the news at the moment. Strikes crippled its Royal Mail operations in December and further industrial action could happen in the months ahead. Also this week it was hit by a huge cyber attack that saw it discourage customers from sending parcels abroad. In fact the courier is fighting battles on a number of fronts. The letters market is famously in a state of long-term decline. And IDS must invest vast sums of money to improve its parcel operations to offset this. It also faces a sharp drop in revenues as Britain’s economy shrinks. This is all the more troubling given the huge debts on the company’s balance sheet (net debt stood at £1.5bn as of September). Online retail looks set to expand steadily over the next decade. And couriers like IDS will play an essential role in this growth. Solid progress at the firm’s GLS international division could also drive profits much higher. But on balance I think there are better cheap UK stocks out there today.