Con lo SharePoint Framework (SPFx) è possibile accedere agli items di una lista tramite l'oggetto SPHttpClient:
import { SPHttpClient, SPHttpClientResponse, ISPHttpClientOptions } from '@microsoft/sp-http';

export interface ILinkItem {
  title: string;
  url: string;
  // altri campi 
}

export default class SPDataService {

  public getListItems(webAbsoluteUrl: string, listTitle: string): Promise<ILinkItem[]> {
    //const url = this._webAbsoluteUrl + "/_api/Lists/getByTitle('" + listTitle + "')/items?$select=Title,Url";
    const url = webAbsoluteUrl + "/_api/Lists/getByTitle('" + listTitle + "')/items?$select=Title,Url";
    const items: ILinkItem[] = [];

    return this._spHttpClient.get(url, SPHttpClient.configurations.v1)
      .then((response: SPHttpClientResponse) => {
        return response.json().then((data) => {
          if (data.error) {
            const err = new Error(data.error.message);
            console.log(err);
            throw err;
          }

          data.value.forEach(item => {
            const urlItem = item.URL;
            items.push({
              title: item.Title,
              url: urlItem.Url,
              // altri campi
            });
          });
          return items;
        });
      });
  }

}
per usarlo nella web part:
import { IDataService, ILinkItem } from './data/SPDataService';
...
private _dataService: IDataService;
...
this._dataService = DataService.get(this.context);
...
this._dataService.getItems("/sites/miaSiteCollection/mioSito", "Mia Lista")
  .then((items) => { ... 
    this.context.statusRenderer.clearLoadingIndicator(listContainer);
    ... 
  })
  .catch((error) => {
    this.context.statusRenderer.clearLoadingIndicator(listContainer);
    this.context.statusRenderer.renderError(this.domElement, error);
  });