Lactulose, breakfast high in fibre, plenty of fluids (especially in conjunction with fibrous food, more effective that way). I definitely know where you're coming from. I'm really trying to avoid straining (due to piles, straining makes them so much worse) but sometimes it just can't be helped. It sucks!
If its there and having trouble coming out then a high fibre diet or oral laxatives would do very little to shift it in short term. This would only give you stomach ache because you have ingested the fibre and nice healthy poo is coming along with no where to go for your blockage. I'd check with your MW or GP first but when this happens to me I use glycerin suppositories which stimulates your bowel to empty. Usually works for me within minutes
The fibre supplement "ispaghula husk" has transformed my bathroom experience. I had dreadful issues and my midwife suggested this. I can't recommend it enough. I either had diarrhoea or constipation and rarely had a normal bowel movement. Since starting this at 20 weeks I've been 1000 times better than ever. It seems to balance everything out. I have one comfortable BM every morning. I'm 36+ weeks now. I'm not sure what the British brand names would be but ask your pharmacist. Drink plenty of water with it too.
BTW, straining is majorly bad for you and will weaken your pelvic floor at a time you need to be strengthening it. Whatever you decide on, make sure you stop straining to go. Best of luck.
Is tricky with a toddler banging on door or DH shouting upstairs 'what are you doing up there?' Unfortunatly if I can't 'make' myself go I get really bad squits a day or so later and nearly pass out from the tummy pain. Hope things 'ease up' for you